"Studierende" is actually a counterexample, because it means "people who are studying right now". So if you hear of "Studierendenproteste" rather than "Studentenproteste" (student protests), you can picture them reading books during their protest. :)

“Student” comes from Latin “studens”, which grammatically is exactly the same as “studierend” (Partizip I in German / Present Active Participle in Latin). The difference in meaning is random.

Heh, but German is not Latin, and so 'student' in German, as often happens with borrowed words, has acquired a different meaning, viz. that of a noun in this case.

Sorry, in Latin every adjective can also be used as a noun. So “studens” (“studierend”) can also mean “Studierende(r)”.

Edit: The point is, Latin “studens” also has the concurrency aspect to it, just as German “Studierender”. If you say “studens ambulat”, it means “He/she is taking a walk, while studying.”

I think you might be reading too much "right now" into "-ende". Counterexamples: Tragende Wand, führende Persönlichkeiten, rollende Landstraße etc.

Doesn't buy you much in the singular case since you gotta pick a gendered article. :/