It's really pretty uncommon to call a chicken sandwich or a sausage breakfast sandwich a "burger." The term comes from the meat inside of it, hamburger, so generally speaking, other fillings will be called a "sandwich" instead of a "burger." I guess you could call those things burgers, but it would be weird.

And no, a "slider" isn't a "small burger" (it can be), it's a sandwich. A burger is also just a sandwich, so calling a specific sandwich a "burger" vs a "slider" means two different things, a "burger" is larger and generally has ground beef (but occasionally veggies or similar), and a "slider" is a small, usually round sandwich.