They do not share any information. You can re-use your essays. In fact, most students do just that. It is too much work to write entirely new essays from scratch for every place on your application list.
Just be sure to have someone else proof-read it before you send it off so that you don’t say “College X is the best place for my to study Y” when the essay is actually headed to College Z, and the major field there is called W instead of Y.