They are all variations on fruit heated with some form of pastry. There are so, so many, but here is a quick run down...
Crumble - fruit with a streusel like topping that is baked until the fruit is cooked. It is similar to a "crisp" but there are oats in the topping.
Crisp - fruit with a topping made up of sugar (or sweetener), butter, spices and flour that gets baked together.
Betty or Brown Betty -fruit (usually apples) baked between layers of buttered crumbs. Originated in Colonial times and usually served with whipped cream or a cream sauce.
Cobbler - fruit with a biscuit topping. The biscuits are dropped on in small rounds, producing a "cobblestone" like texture when the mixture bakes. It can be made with cookie dough or even cake batter.
Grunt - uses the same ingredients as cobblers, but instead of being baked, is cooked on a stove or fire. The fruit is stewed then the biscuits are added and the lid is placed on the pan. They "steam" cook. The sound is makes as steam escapes sounds like a grunt.
Slump - same thing as a grunt, but named for the way it slumps when plated.
Buckle - starts out with the pastry mixture on the bottom and the fruit on the top. During the baking process, the pastry rises and buckles around the sinking fruit.
Pandowdy - Fruit is covered with a rolled pie crust. Then the desert is baked. Once cooked, you break the crust or "dowdy" it with a fork. The edges get soft, absorbing the crust while other parts stay crispy.
Sonker - a deep dish pie with a batter topping, common in the Carolina's. What makes this dish different is that there is a higher proportion of fruit to topping.
Clafouti - usually considered baked pudding. This originated in France. Fruit is topped with batter and baked. The fruit sinks in between batter.
Bird's Nest Pudding or Crow's Nest Pudding - cored apples are placed in a baking dish and the cores are filled with brown sugar. Then a batter is poured around the apples and into the cores and everything is baked. An old fashioned early American "baked pudding".