archness vs fun

archness and fun both are nouns.

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

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

Other hypernyms of archness include playfulness.

archness (noun)	fun (noun)
inappropriate playfulness	activities that are enjoyable or amusing
	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)