fun vs funniness

fun and funniness both are nouns.

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

As nouns, funniness is a hyponym of fun; that is, funniness is a word with a more specific, narrower meaning than fun:

fun: verbal wit or mockery (often at another's expense but not to be taken seriously)
funniness: a comic incident or series of incidents

fun (noun)	funniness (noun)
activities that are enjoyable or amusing	a comic incident or series of incidents
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)