I think someone has been drinking too much coffee, but by request we have seep and percolate, and I'll add steep for the tea drinkers out there.
Seep comes from the Dutch "sijpelen" for "to ooze". Then through the German "sifen" to Old English "sipian", until finally, c. 1500, "sipe" by way of a diatectic variant became seep. Still meaning to ooze, though. Whew. Meanwhile, percolate came solely from the Latin "per" meaning "through" and "colare" meaning "to filter" (from "colum" for a "sieve"). Now, both mean that some liquid passes through small openings, but seep has the liquid coming through on its own and at it own rate, while in percolate, the liquid is forced by something (usually thought of as heat). That's it. I will make one observation that percolate tends to have a connotation from certain usage that the liquid has to go through the porous material more than once, but the etymology and derivation only require that the liquid be forced. The number of times, even as few as once, is irrelevant. Now, steep, as a verb, has a questionable etymology from the Old Teutonic "staupjan" for the vessel storing liquor OR from the Danish "stope" or the Norwegian "stoypa" for "to steep" when used in reference to malting, although OED opines that these Scandanavian reconciliations have a basis in "cast down" relative to metals into molds. I suppose its not a great leap to derive that molten metal might have a tendency like other liquids to earn this definition, but steep is more akin to the process of diffusion as may be involved in fermentation. Regardless, steep, in contrast to seep and percolate, simply involves dunking or soaking in a liquid for the process of extracting impurities or flavor.
So, the usages are fairly straightforward. If I were to drink coffee, I would percolate water through the grounds, whereas since I usually drink tea, I just steep the teabag in nearly boiled water. If my cup is broken, either drink might seep onto the table. Ok, those are the obvious sentences. A hot bath does wonders to steep the tension from my shoulders. Possibly, although it would be more acceptable with something that could actually be leached from your system. A hot bath does wonders to steep toxins from my skin. After a long performance, sweat practically seeps from my body. Hmm. Perhaps overly graphic, and seep has the connotation of being a little thicker in proportion to the size of the porous material to account for the slow rate. Sweat isn't ever thick, and skin is really quite porous, so the better physical usage would be after a pricking my finger, blood seeps from the wound. However, sweat might percolate from my body in a sauna. The forced aspect has no relation to the size of the porous material; only that the liquid is coming out at a faster rate than normal. Now one might argue that in a sauna, the liquid is coming out at a rate commensurate with the temperature, and there is no "forcing", but why else does one go into the sauna if not to force sweat?
Now, this wouldn't be a regular post if I didn't try to expand the usage. So, these words all derive from liquids, so anything that could act like a liquid is also fair game. Mice seep from a hole in the wall or percolate through the walls? Maybe, but not likely. Animates (even a stream of animals) and tangibles are hard to analogize like liquids. But intangibles are fair game. While writing my opposition to Plaintiff's counsel's motion for summary judgment, a myriad of arguments and ideas percolated from my mind, and seeped onto the page. And then, after losing his ridiculous motion for summary judgment, Plaintiff's counsel steeped in his own humiliation and anger.
The problem is, though, that, aside from intangible usages, percolate has taken on a very specific identity with coffee, while seep and steep have broader usages more generally. Although technically correct that when I squeeze my teabag before removing it from my cup that I am percolating the tea, that just conjures vile tastes in my mind of mixing coffee and tea, and no self-respecting tea drinker would do that. Meanwhile, steep can be used to describe infusing flavors (the pineapple was steeped in vodka), and seep for anything that is leaking (milk is seeping from the carton).
Hopefully, you will find that your vocabulary is steeped with good words, which may percolate to others and seep into better usage.