There are two species of werewolf in Twilight canon. One, the Children of the Moon, gets no screentime or detailed treatment at all. They were from Europe and are now presumed extinct, killed off by some vampires at the behest of one vampire who didn't like them.

The other, the Quileute tribe wolves, features more heavily. Their older legends don't use the word "werewolf"; the ones who show up in the story call themselves werewolves because that is the obvious modern American thing to call a person who can turn into a giant wolf. The "wolf" part in particular was an arbitrary selection made when the species came into existence; they could have been bears or eagles or voles or something instead. So the technical term for them is "shapeshifter", but this doesn't overcome the sheer obviousness of "werewolf". This is all canon or obvious extrapolation therefrom, not fanon.