fun vs wit

fun and wit both are nouns.

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

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

fun: verbal wit or mockery (often at another's expense but not to be taken seriously)
wit: a message whose ingenuity or verbal skill or incongruity has the power to evoke laughter

Other hypernyms of fun include humor, humour, witticism, wittiness.

fun (noun)	wit (noun)
activities that are enjoyable or amusing	mental ability
violent and excited activity	a message whose ingenuity or verbal skill or incongruity has the power to evoke laughter
a disposition to find (or make) causes for amusement	a witty amusing person who makes jokes
verbal wit or mockery (often at another's expense but not to be taken seriously)