Isn't the term "cosplay" just for the anime folks? Shouldn't superhero costumers have their own term?

Sort of. A lot of costumers of the mainstream books/shows prefer the term "costumer" exclusively; others don't mind sharing the term "cosplay." I typically don't "get into character" and I don't "do skits" like the anime people but I'm just used to the word cosplay and it makes searches/hits easier.

Ask me anything but seriously think twice about rude or insulting remarks.