I assume you are referring to the terminology as introduced by Meszaros. Martin Fowler does also mentions them regularly. I think he explains the difference pretty well in that article.
Nevertheless, I’ll try again in my own words 🙂
A Fake is closer to a real-world implementation than a stub. Stubs contain basically hard-coded responses to an expected request; they are commonly used in unit tests, but they are incapable of handling input other than what was pre-programmed.
Fakes have a more real implementation, like some kind of state that may be kept for example. They can be useful for system tests as well as for unit testing purposes, but they aren’t intended for production use because of some limitation or quality requirement.