Oh, perhaps they do. I don't think you should lump mushroom species though, as the rules for distinguishing the related species from inedible species will be different.

Yeah, but they do it all the time. Like morels - there are tons of different morels, but we typically use "morel". Or for boletes, same thing. Even puffballs, oysters, etc. Even chanterelles have a bunch of different species that it refers to.