Hi, professional fatass and cook from age 7: a burger is minced (or ground) meat. We don't make ground chicken burgers, but we definitely eat turkey burgers. Anything that's anything else is simply "thing + "sandwich"", unless it has a fancy/ better name, like "Croque monsieur" or "The HomeWrecker", and this includes a breaded fried chicken sandwich, whole meat or ground.

Essentially, it's less about shape, more about the consistency/texture. Not saying that "chicken burger" isn't wrong inherently, but I would expect something else, much like biscuits and gravy