fun vs jocularity

fun and jocularity both are nouns.

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

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

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