There's not much of a difference at all. They basically have the same meaning. Fun is the feeling of enjoying yourself. So if you were to say "Did you enjoy yourself at the party?" or "Did you have fun at the party?" both would be completely fine.

Although there are some instances where fun and enjoy are not interchangeable. For example, if you told a joke to your friend and he didn't react the way you wanted, you might say something like "you're no fun". In that case, you wouldn't be able to use "enjoy".

Well, your friend didn't think it was funny even though you wanted him to think it was and laugh. He's killing the fun of the moment so you might reply "you're no fun". But the tone of this expression in this situation is playful. If I had to connect it to an expression it would probably be this: (´ε｀ )


Sorry...I'm probably not explaining it clearly. Let me know if it's confusing.