Additionally, I'd say both words are used to connect. The word "however" (adverb) connects the meaning of the two clauses. The word "and" (conjunction) joins the two clauses together in order to make them part of the same sentence. It is only necessary to connect the clauses once with one word. Don't try to connect them twice. It doesn't work.
"He found his wallet; however, he still left the auction."
In this sentence, the meanings of the two clauses are connected.
"He found his wallet and still left the auction."
In this sentence, the two clauses are connected so that they can be two equal parts of the same sentence.
We could say: He found his wallet and he still left the auction.
I would use "still" only for emphasis.
"He found his wallet and he left the auction."
I think using "still" implies that there was reason to believe he might have stayed, but decided to leave after all. Staying was conditional upon finding his wallet.
If we don't use "still", it would just mean that he had no intention of staying necessarily. We are almost 100% certain that he knew he was going to leave after he found his wallet.