A slider is a small (cheese)burger
American Swiss cheese is specifically AOC excluding (as it is emmentaler style but not from there, so it cannot be called that). it uses the same techniques (copper cooking vat, large wheels, etc.) - it's a simple catchall term for a generic, alpine style cheese typically made in the US
bread hardens as moisture is lost from (re)heating, which hardens the crust and interior as moisture and air escape