Stub
I believe the biggest distinction is that a stub you have already written with predetermined behavior. So you would have a class that implements the dependency (abstract class or interface most likely) you are faking for testing purposes and the methods would just be stubbed out with set responses. They would not do anything fancy and you would have already written the stubbed code for it outside of your test.
Mock
A mock is something that as part of your test you have to setup with your expectations. A mock is not setup in a predetermined way so you have code that does it in your test. Mocks in a way are determined at runtime since the code that sets the expectations has to run before they do anything.
Difference between Mocks and Stubs
Tests written with mocks usually follow an initialize -> set expectations -> exercise -> verify pattern to testing. While the pre-written stub would follow an initialize -> exercise -> verify.
Similarity between Mocks and Stubs
The purpose of both is to eliminate testing all the dependencies of a class or function so your tests are more focused and simpler in what they are trying to prove.