What is the exact difference between 'Adapter' and 'Mediator" patterns?

I know that Adapter is a structural pattern and Mediator is a behavioral one. But as far I understood, what both of them are doing, is connecting two (or more) other classes which are potentially incompatible (not so maintainable) for direct communication.

Can some one give a close comparison between these two and point out the exact difference?

These are the links for Adapter and Mediator explanations in TutorialsPoint.