Fun is peanut butter ice cream.
On a more serious note
A subjective emotional experience, I'd say.
You might enjoy something, I think, without calling it fun. ie, a horror movie. I'd guess there's some distinction between "fun" and "enjoyment".
A person might enjoy physical conflict such as boxing / martial arts ringfighting, because it's exhilarating and challenging. But I doubt they'd call the experience of hitting and being hit "fun".
A person might also enjoy pain in a sexual context, and get huge amounts of pleasure from it. But still not calling it "fun". Maybe satisfying, but not fun.
But fun always includes enjoyment, I think.
Just some random thoughts for now