Pertinent comes from the Latin "per" meaning "through, by" and "tenire" for "to hold". OED adds that the Latin "pertenere" means "to extend, stretch, tend (to), belong (to)". By c. 1350, the Old French "partenir" for "to belong or have a connection to" emerged through the Middle English "pertenen" then to our current "to be applicable". Of course, like all bad dictionary definitions, Dictionary.com (née Doctor Dictionary) has defined pertinent as relevant, and even OED has a tertiary but current definition that "pertinent" is "pertaining to the matter at hand, relevant, to the point".
Meanwhile, relevant comes from the Latin "re" for "again" and "levare" for "to raise up" a derivative of "levis" for "light in weight", and is related to the word "relieve" meaning "to lessen the effect of something" as from physically and then metaphorically lifting the burden and "levity" for "lightness". So, how this came to have any meaning or relationship to either things or ideas is still a mystery. OED adds an interpretation of "relieve" of "to assist", and perhaps from there, we can grasp that something that is relevant is intended to assist the person and later, the reader/listener. However, even OED defines "relevance" as "pertinent important to current issues", and "relevant" as "bearing upon, connected with, pertinent to the matter in hand" which only muddies the waters, and provides a specific legal meaning of "relevant" as "legally pertinent or sufficient". At this, I throw my hands up and cry 'tautology'.
Back to OED. Obsolete definitions of pertinent included "pertaining or belonging to as a possession, dependency or appendage, or as a part, constituent or function" and "appropriate, suitable in nature or character". The former definitely derives from the "holding" of something physical, while the latter begins the slide into the intangible as we go from the nature and character of something physical to the nature and character of something abstract, and ultimately to a definition which includes "relevant" to a specific issue (to a matter at hand or a point). Whereas, there are no significant obsolete definitions of relevant, which has, therefore, been as to a specific issue (to current issues or a matter at hand) since c. 1560. This leads to an inference as each word began with a physical application (holding, raising) that, as the word's usage drifted into intangibles and abstract concepts, the application got narrower to allow for the lack of obvious identification of the relationship between the subjects being related. Great. Both words now relate to intangibles and abstract concepts with narrow applications.
Back to the etymologies. Pertinent with "belonging" has a element that the thing or idea is part of a greater group or whole, while relevant with "lessening" as of weight is not part of a group, but merely assists the group or whole. Pertinent might even be integral, without which the greater group or whole is incomplete, while relevant is helpful, but without which the group or whole will go on. Finally!!! A distinction. But it does also suggest that pertinent is a subset of relevant.
So, hold on. It is going to be a bumpy ride while I try to use these.
Bob was pertinent to the discussion. Probably not, since Bob alone, without more description, does not necessarily connote a person who is intrinsic or required for the discussion. Bob, the CEO of BigCorp, was pertinent to the discussion of the merger with SmallCorp. Bob is now more critical to the discussion because of his title/position. Bob, the mailroom attendant was pertinent to the discussion of the merger. No. No one expects that someone from the mailroom is important enough to be involved such a discussion, unless this is Undercover Boss. Bob was relevant to the discussion. Rather generic, and therefore, arguably true. Bob, the CEO of BigCorp, was relevant to the discussion of the merger with SmallCorp. Now, we disparage Bob's position which is obviously important to any significant business dealings, and possibly engage in a degree of sarcasm about Bob's relative lack of importance. Bob, the mailroom attendant was relevant to the discussion of the merger. Possibly, but only if Bob had certain helpful information as result of his work in the mailroom. Let's see what happens when we stop using "to be". The pertinent teacher discussed Bob's poor math scores. A little esoteric. Why wouldn't you just say the math teacher. The pertinent teacher discussed Bob's behavior issues. Better, because pertinent is modifying teacher, it presumes that there is more than one teacher dealing with Bob, and therefore, suggests that there is one teacher from this group who had knowledge of these specific issues to be able to discuss. The pertinent janitor discussed Bob's...anything. This makes no sense. One would not expect a janitor to be in a group of people who had any connection to Bob to be elevated to this level of discussion. However, the relevant teacher discussed Bob's poor math scores. Still odd because one would presume the math teacher would have this distinction, and not anyone else. The relevant teacher discussed Bob's behavior issues. Yes, but this sounds like there are a pool of teachers who could have discussed the issue, but one was better. The relevant janitor discussed Bob's math scores. No. The relevant janitor discussed Bob's behavior issues. Possibly, if the janitor had information which could be helpful. Now, just to be cute: The pertinent Sith Lord dealt with the transgression. Well, since we all know there are only ever two, a master and an apprentice, and pertinent separates one or more from a group, this is contradictory, and therefore, wrong. Similarly, relevant doesn't work either. As long as there could be sufficient specificity of the person or job description, but not absolute uniqueness in context (pertinent president v. pertinent president at the G8 summit), pertinent can be used. Relevant being broader works in all cases, except when the uniqueness is inherent and/or obvious and therefore, diminishes that quality.
Now, that we have exhausted people, let's try other sentient beings. The kitten was pertinent to the litter. Not really. To parallel the previous sentences, the kitten must do something for the group. The litter was pertinent to the kitten. Ooh, well, yes, because if we rewrite it out of passive voice it becomes something like: the kitten found the litter pertinent. And the kitten would need or want to be part of the litter. But is uniqueness or specificity implicated? Not really, but it still works perhaps because the importance is so high for the kitten relative to the litter. The kitten was relevant to the litter. Probably, still generic that it could mean anything. The litter was relevant to the kitten. Same. Even if we rewrite it, the kitten found the litter relevant. Yep. Moving on. The cat was pertinent to the mouse population in the area. Ok. Was this a super-mouser? The cat was relevant to the mouse population in the area. Yes. The worker ant was pertinent to the colony. No, too vague. The worker ant was pertinent to the queen's well-being. Still no, because we know the worker ant does not have a specific enough job. I'm not sure there is anything the worker ant could do that would be pertinent. The worker ant was relevant to the colony. Vague, and therefore, probably true. The worker ant was relevant to the queen's well-being. Still vague, and therefore, probably still true. The seeing-eye dog was pertinent to Bob's well-being. Yes. The seeing-eye dog was relevant to Bob's well being. Also, yes, but given the inference that Bob is blind, and knowing the unique relationship between a seeing-eye dog and its owner, the specificity of the task raises it to a level of pertinent. This is not dissimilar to multiple CEOs of a corporation over the life of the corporation.
On to the inanimate. The pertinent bolt was missing from the gate and thus, it would not stay closed. Yes, without this bolt, the gate does not function, although the usage is a little esoteric. The relevant bolt was missing from the gate, and thus, it would not stay closed. Also yes, but for a different reason, inasmuch as multiple bolts could fill the function. The puzzle was missing a pertinent piece. Yes, because a puzzle is comprised of set of unique pieces without which the puzzle is incomplete. The puzzle was missing a relevant piece. Yes, technically, but not as good because while the missing piece would be helpful to finishing the puzzle, really helpful, and there might be other ways to finish it (trace the missing piece and request a replacement), the piece is a critical element. So, we can see by usage that pertinent works for a thing obviously comprised of other component parts--decks of cards, games, Ikea furniture, computers, cars, houses--where any part or parts are required for the completion of the whole. Having assembled the pertinent ingredients, the chef began to make the recipe. Yes. Having assembled the relevant ingredients, the chef began to make the recipe. Also, yes, but without the gravitas that these ingredients are necessary to the recipe. Without all the pertinent ingredients, the chef could not make the his signature omelette. Without all the pertinent ingredients, the omelette was just scrambled eggs. Yes. And just for completeness: Eggs are a pertinent ingredient to an omelette. But all these sentences are still varying degrees of correct. One can only know the range by exploring the fringes, which means seeing when usage fails. However, writing bad sentences which demonstrate this failure is actually hard.
The pertinent apple was missing from the tree. Grammatically correct, but utterly nonsensical for usage. What makes this apple special, or the absence of the apple makes the group of apples on the tree, or even the tree itself, incomplete? Was this the only one which had a worm? We can't tell that from context, and with any context, this is just silly. The relevant apple was missing from the tree. Again, grammatically correct, but also useless without any context. So, by themselves, these words have an inherent comparison of what they do for the other noun(s) in the sentence. If the pertinent apple were missing from the fruit bowl. Again, what makes this apple special that its absence from the fruit bowl makes the latter incomplete? Was it the only apple? But if it were the only apple, we wouldn't use pertinent; we would use only and be discussing apple thieves or hungry artists. The relevant apple was missing from the fruit bowl. Same. There still isn't enough specificity to the group. Tree was too generic, and especially with the overtone of it being an apple tree, there were too many equal apple substitutes. Fruit bowl suggested a smaller group, but not enough that the apple was critical. And relevant in each instance was just too broad to be useful to the generic apple and the group. She found the pertinent book in the library. Ok, this may have legs inasmuch as a library does not usually have more than one volume of the same book so each book is presumptively unique and part of the greater collection of the library. She found the relevant book in the library. No. Because of the uniqueness of the collection of books in a library, pertinent should be used. I will note, however, that our ear hears relevant in this sentence as correct. She found a pertinent book in the library. Awkward and bizarre because each book would be unique, and therefore, every book she found would technically be pertinent to the library, otherwise, why was it there??? She found a relevant book in the library. Correct. She found a pertinent book on the history of cats in the library. Yes. This book has answered all the questions she had about the topic, noting there may be more than one pertinent book, but you wouldn't have to read more than one. She found a relevant book on the history of cats in the library. Yes. But this one is merely helpful on the subject. A Google search may give you a lot of relevant articles, one or more of which may be pertinent. Yes, of course. In short, pertinent connotes that the thing is a necessary element, while relevant may be optional.
So, just going back a few sentences, let's examine "a" versus "the" with these words. A pertinent teacher discussed Bob's behavior issues. This still works, but now the teacher is one of a subset of teachers who can discuss Bob's issues. A relevant teacher discussed Bob's behavior issues. Still part of a subset of teachers, but with less gravitas than pertinent, but only if we hear them in comparison. Otherwise, relevant would probably be used. The same is true with cats: Mnemosyne is a pertinent cat to the mouse population versus Mnemosyne is the pertinent cat to the mouse population. The former makes her one of the subgroup known as mousers, and the latter makes her super-kitty, unless we limit her scope of activity to the house, in which case it is absolutely correct as Metis doesn't want to get her white paws dirty. Mnemosyne is a relevant cat to the mouse population. Mnemosyne is the relevant cat to the mouse population. Yes, and yes, but without as much impact if one understands the inherent contribution connoted by pertinent. Otherwise, all cats are relevant to mice, even as observers. A pertinent apple was missing from the tree. Now, it could be the only ripe one, or the only one with the worm, or some other unique characteristic. The pertinent apples were missing from the tree. One might suspect this could be said after all the ripe apples were picked. A relevant apple was missing from the tree. Still grammatically correct, but useless without any context. I already did the book in the library and the actor. However, if the man had only given a pertinent detail to the sketch artist, that would be accurate, and suggest that it was a very important detail (a tattoo or a scar), as opposed to the man giving a relevant detail (height, weight, hair color).
Now, I know I have gone into extreme detail on this particular entry, but I need to add one more detail. As I mentioned, there is a specific legal meaning of relevant, and which is why I have deliberately avoided any sentences with Plaintiff's counsel. Legally speaking, relevant is used as a catchall. The relevant documents. The relevant testimony. The relevant cases. This isn't just what would be helpful or optional. These are required and often unique in nature, for which pertinent would otherwise be used. Additionally, the use of relevant in law breeds the use of relevant. We track the language of the case/statute in writing for the most persuasion (briefs) or best future enforceability (contracts). I would suggest that the pervasive introduction of legalese into the mainstream has contributed to the increased non-use of pertinent. So, for sake of completeness: Plaintiff's counsel provided the relevant documents in response to her discovery requests. Yes, absolutely. Plaintiff's counsel disclosed the pertinent witness. In law, no, otherwise, yes. This is always relevant. Now, keep in mind that the use of relevant instead of pertinent is only when actually used in law. Otherwise: The pertinent parties were present in court, while the relevant witnesses gave testimony. Yes, since this is an outsider's narration of the events. The pertinent vote of the board ratified the new member. Yes. The vote was required to allow the new member to join and become part of the whole. The relevant vote of the board ratified the new member. Also yes, but doesn't have the gravity that the vote was required. Maybe now, maybe later. As a lawyer, however, I would get the requirement from the use of the word ratified, but if this is being documented in the minutes which are legally required or described later to prove that the vote was appropriately conducted, then it would be the relevant vote simply because of the legal context.