I saw a gentleman on the bus (who didn't look Jewish) find a book next to him on the bus, and take it with him (with what looked like the intention to read it). I suspected him of being both non-Jewish, and not a תלמיד חכם obviously. I don't think that was right of me. It could be he was Jewish, and just didn't see any (halachic) point in wearing a head covering. It could also be he was somewhat of a תלמיד חכם because he knew the law that he was allowed to take it, etc.)
I think the definition of "תלמיד חכם" means someone who learned well from their "רב" (Master). It does denote being a "good student", but more than that, a disciple of a "חכם". In Hebrew חכמה denotes knowing a certain amount of information, so it would mean; "someone who keeps the information that they were taught and that they reviewed (ששינן) by the חכם". The חכם himself was and is also still a "תלמיד חכם", but now he's less of a student and more of a conduit of knowledge.
(Latter addition: The Rambam says a talmid chacham should cover his head; could be that's where the idea that everyone should (halachicly) cover their heads came from).