Nothing really, but in the minds of many the difference is in formality. Educated means having received an education. Of course a self-educated person is educated. The same minds would aver that learned (pronounced learn-ed) is the man possessing a great body of knowledge of a scholarly nature.
In law school we studied cases and opinions written by the great Appeals Court Justice Learned Hand. I will never hear the word learned without that memory popping up. I always wondered........What was his mother thinking?