Partial Class vs Extension Method

I dont have much experience of using these 2 ways to extend a class or create extension methods against a class. By looking others work, I have a question here.

I saw people using a parital class to extend an entity class in a project. Meanwhile, in the same project, there is another folder containing a lot extension methods to the entity class.

Is it right to do so? I mean these 2 ways both work well. Could you give me some real practice how to pick one from them when I want extend a class?