fun vs jocosity

fun and jocosity both are nouns.

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

As nouns, jocosity is a hyponym of fun; that is, jocosity 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)
jocosity: fun characterized by humor

fun (noun)	jocosity (noun)
activities that are enjoyable or amusing	the trait of merry joking
violent and excited activity	fun characterized by humor
a disposition to find (or make) causes for amusement
verbal wit or mockery (often at another's expense but not to be taken seriously)