The difference between fun and funny is not simply that fun is a noun and funny is an adjective. True, fun is a noun, and we say that we ‘had fun’. But it is also an adjective where we describe things as being fun. It means enjoyable, and has nothing specifically to do with laughing.
So, we might say, “Swimming is fun”. We wouldn’t say, “Swimming is funny” unless, of course, you are laughing like a crazy person in the pool!
Funny means that something made us laugh, so for example, Mr Bean is funny. Or “I saw my friend slip over on a banana skin and it was so funny!”
Here are the two together:
“I went to a football match last week and it was good fun. During the match, the referee fell over and it was really funny.”