All the dishes Cobbler, Crumble and Crisp are all similar but there are some differences.
Cobbler is a dish consisting of fruit or savory filling poured into a large baking dish covered with batter, biscuit or dumpling before being baked.
The Crumble might be known as a Brown Betty and is of British Origin. It can be sweet or savory. The Crumble is CRUMBLY and is a mixture of usually butter, flour and sugar. Savory crumbles are made with cheese. Just think about crumb tops.
A Crisp really is a crumble but is usually made with oats and some sort of nuts.
A lesser known dessert that is related is a Pandowdy that is a deep dish spiced apple dessert covered with a rich crust.
That is the Forking Difference between a Cobbler, a crumble and a Crisp.