A cobbler is like a pie filling, but without the bottom crust and it is usually much thicker, or higher or taller, than a pie. A crumble is usually a pie with a top crust that is crumbly. It is a crumbly, crunchy topping instead of a pie shell. read more
Cobbler: baked fruit topped with a batter or biscuit crust. The topping is often "cobbled" rather than smooth; the topping is generally dropped or spooned in small clumps over the fruit, allowing bits of the filling to show through. read more
The original difference between the two lay in the streusel topping: crisps would contain oats and crumbles would not. In an actual crisp, as in apple crisp or strawberry crisp, the oats in the topping crisp up as it bakes, hence the name. read more