fun vs frolicsomeness

fun and frolicsomeness both are nouns.

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

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

fun (noun)	frolicsomeness (noun)
activities that are enjoyable or amusing	lively high-spirited playfulness
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)