A "wet market" is just a market, like the ones we have all over England that sell fresh vegetables and meats in the open. In Taiwan, where I lived for four years, they're called (in English translation) "traditional markets", in Mainland China they're called "wet markets".
During my four years living in Taiwan and exploring China, I never once saw a wet market selling wild animals, except snakes (which was rare). When I asked Chinese friends about wild-animal consumption, they would respond in one of two ways: 1) Genuine hurt and bafflement that people associate China with such barbaric practices; 2) Explain that it happens somewhere "out there", in the vastness of China, but only by a few mad old men who still think they live in a poverty-stricken backwater where they're forced to eat whatever moves to survive (or so they've heard, as they've never actually met somebody who eats bats or dogs).
I don't doubt that some Chinese wet markets do actually sell wild animals, but they're not this widespread "problem" all over China the Western media makes then out to be. "Wet market" doesn't mean "market that sells wild animals", it just means "market". I speak reasonably proficient Chinese, but I only became aware of this alleged association between "wet markets" and "wild animals" this year.