Interesting, Jesús. Yes, as I understand it, "divertirse" is kind of related to entertainment/distraction (at least, that's how it is in my mind) and "disfrutar" is more closely associated with taking pleasure in something.
I see, so for you, "having fun" is about a louder, more obvious, easy enjoyment, and "enjoyment" is calmer, more moderate. I don't know if I use the same distinction, but I agree that there is a distinction. To me, enjoyment seems more refined and related to pleasure, while "fun" has a childish connotation, at least in my mind.
When people ask about my hobbies, and I say that I like reading and languages, they answer, "Yes, but what about for fun?" Well, that is fun for me!
I agree that between cultures, people have different notions of fun/enjoyment, but it's also quite individual within cultures themselves.