I'm pretty sure I've seen on menus burger-like items containing chicken, called a grilled chicken sandwitch. Now I could be remembering wrong, but I am pretty sure these things were on buns, not normal bread, so that can't be the dintinction.

This is the kind of sandwich I was eating last night -- fried chicken breast on a hamburger bun. On some menus, these types of sandwiches are listed in the burger section, but at this particular restaurant it was listed with the sandwichs, and burgers had their own separate section.

I think the main difference between these sandwiches and burgers is the meat being ground and formed into a patty shape. But, as others have mentioned, this leaves us with gray area regarding other ground meat sandwiches -- meat loaf, spam, sausage. I'm not sure what the difference is here.