Adverse possession, you get to take control of the land and retitle it with a legal description after going to court. You then own it going forward and can deny the previous owner access, as well as everybody else. You legally steal someone's property by using it, planting it, mowing it, improving it for a certain period of time.
Prescriptive easement, you get to keep crossing the property on the trail or road that has existed historically even as the exact path may shift with erosion etc. It's open to travel, but the surrounding property owner hasn't lost title.
At least that's as I understand it... as a non lawyer. If I've muddled anything with my non-legalese, one of the sharks can straighten me out.