Well, this comparison came up quite sporadically from a book I wasn't reading, but got dragged into discussing notwithstanding. Apparently, the word sempiternal required just slightly less than forever to process...you'll get the joke later.
Sempiternal comes from the Latin contraction of semperaeternus for "semper" meaning "always" and "aeternus" for "eternal" from "aeviternus" meaning "of great age". This might seem redundant on first blush. Of course the immediate question is what could be less than eternal that it would require a modifier of always, and then if sempiternal means always eternal, what does mere eternal mean? Eternal, like all the crazy connotations, evolved in the Middle Ages, c. 1350. Sempiternal came about 100 years later, c. 1450. If the connotations are to be believed, sempiternal refers to an enduring thing which came from a known beginning, while eternal refers to something which had neither a beginning nor an end. But the definition of sempiternal is hazy, at best, and doesn't make the distinction as clearly as the definition of eternal implies. Moreover, sempiternal notes that the definition if "literary", as if to imply that only if you are a published writer/author could you possibly use this word. Perhaps the real intention was only if you were a published writer/author would you possibly use this word...
I have to confess that, as of late, my tolerance for idiotic and obtuse etymological evolutions has become strained. And OED is just so heavy and awkward. But, OED confirms that sempiternal is to "endure without end", implying that it had a beginning, and eternal is "infinite in past and future duration". Pretty clear now, although still potentially useless.
Diamonds are not forever; they are merely sempiternal. Yeah, that's romantic. Many arguments by Plaintiff's counsel seem sempiternal. There are rules requiring cases be disposed of within a prescribed period so they do not take on the appearance of sempiternality. A postings to the internet automatically becomes sempiternal. Ok, you get the picture. Meanwhile, very simply, a concept that has no known beginning as well as no known end would be eternal. Love is eternal, even if the diamond isn't. Arguably, murder is sempiternal from Cain and Abel, but revenge according to the ancient Greeks was eternal. And of course, there is the eternal line at the Registry of Motor Vehicles. yes, that one was sarcastic. But while the difference is definable and clear, use sempiternal in causal, non-literary circles, and you will draw more blank stares than using animadversion. I'll save an analysis of "forever" for later to see if that word may be used as a catch all.