sense of humor vs fun

sense of humor and fun both are nouns.

Word	Noun	Adjective	Verb	Adverb
sense of humor	Yes	No	No	No
fun	Yes	No	No	No

As nouns, fun is a hypernym of sense of humor; that is, fun is a word with a broader meaning than sense of humor:

sense of humor: the trait of appreciating (and being able to express) the humorous
fun: a disposition to find (or make) causes for amusement

Other hypernyms of sense of humor include playfulness.

sense of humor (noun)	fun (noun)
the trait of appreciating (and being able to express) the humorous	activities that are enjoyable or amusing
	violent and excited activity
	a disposition to find (or make) causes for amusement
	verbal wit or mockery (often at another's expense but not to be taken seriously)