We don't know that the OP is talking about AQHA showing, it might be 4-H, a local show organization or a different breed organization. But I will agree, fitting and showmanship is usually about the handler demonstrating their skills at presenting the horse.
A medal class in the equitation world is either mini medal, 3ft, or a big eq medal, such as Pessoa Medal, 3'6. There are different phases depending on the class, there is an over fences phase, then either a test, which the judge tells you, or a flat phase. Limit is what maura said. Bridle path hack is a class in the pleasure division usually, in hunter land anyway. I believe they can ask you to halt and back up, or jump an itty bitty cross rail. Hope that helps