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

Question

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.

And these are sourcemaking explanations. Adapter, Mediator.

Answer 1

JB Nizet already wrote a good answer. I just want to explain the differences in simpler words:

• Mediator should be used when you don't know how to communicate with other objects or you aren't allowed to

• Adapter should be used when you know exactly how to communicate with objects, but these objects might not support some communication methods or differ