1. Something that provides mirth or amusement. A picnic would be fun.
2. Enjoyment or playfulness. She's full of fun.
They are awfully close in meaning yet are not interchangeable. Both nouns, FUN seems to require an event, such as enjoying the company of family and friends. But after the event is over, has the FUN stopped, leaving you with a feeling of HAPPINESS as you remember the good times?
Of the two, I think I prefer HAPPINESS to FUN simply because of its "staying power." I can be happy for no particular reason other than I woke up to a lovely morning. HAPPINESS doesn't require an amusing event to be my current state of mind.
It's FUN to write fiction and it makes me happy when my words flow smoothly onto the screen, but I can experience HAPPINESS while executing mundane tasks like folding clothes, too. Folding clothes is not a particularly FUN chore, but I can be happy doing it.
Dave and I have FUN playing cribbage but just being with him gives me tremendous HAPPINESS. My cats make me happy, even when I am not having FUN playing with them.
And while FUN requires amusement, HAPPINESS is more of a personal choice. Despite your own present circumstances, no matter how much or how little you have in the bank, you can choose to experience HAPPINESS. The whole "Attitude is Everything" axiom.
But wait--can't you also choose to have FUN? yes, but again, it requires amusement. You could swing on a swing or attend a party and choose not to have FUN, but you had to get on the swing and attend the party first.
So I'll take HAPPINESS over FUN anytime. It's something I can generate on my own, even if sometimes it can be a challenge to do so.