inaptness vs inappropriateness

inaptness and inappropriateness both are nouns.

Word	Noun	Adjective	Verb	Adverb
inaptness	Yes	No	No	No
inappropriateness	Yes	No	No	No

As nouns, inappropriateness is a hypernym of inaptness; that is, inappropriateness is a word with a broader meaning than inaptness:

inaptness: inappropriateness
inappropriateness: the quality of being not particularly suitable or befitting

Other hypernyms of inaptness include unworthiness.

inaptness (noun)	inappropriateness (noun)
inappropriateness	the quality of being not particularly suitable or befitting
	inappropriate conduct