There is raw fun, a sort of fun that you crave when you get tired of doing serious stuff and want to relax/release yourself. Being serious in this case is out of question.
Then there is hobby, which is similar, but with added level of seriousness on top of it. The fun you get out of hobby varies, but its often different to raw fun. Most of the niche music isn't quite exactly fun, for example. It can be engaging, but in a different way.
This isn't absolute though. Different people in engage in the same activity for vastly different reasons.
For instance, when I play poker, I play it to relax and have some fun with my friends. I have one friend who is more or less a pro poker player though, as in poker (both on and offline) is his main source of income. He regularly goes to tournaments and stuff.