fun vs frivolity

fun and frivolity both are nouns.

Word	Noun	Adjective	Verb	Adverb
fun	Yes	No	No	No
frivolity	Yes	No	No	No

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

Other hypernyms of fun include frivolousness.

fun (noun)	frivolity (noun)
activities that are enjoyable or amusing	acting like a clown or buffoon
violent and excited activity	something of little value or significance
a disposition to find (or make) causes for amusement	the trait of being frivolous; not serious or sensible
verbal wit or mockery (often at another's expense but not to be taken seriously)