fun = entertaining (for example, a party, a movie) funny = amusing (for example, a joke / an situation)

Fun it means you're enjoying while funny it's like you're being humorous or that you make someone laugh.

For example you went to amusement park and you're having fun(enjoyed the surroundings) it's a feeling actually.. Funny, like the very famous Mr. Bean, he's very funny that he can make us all laugh.. ☺