inappropriateness vs ineptness

inappropriateness and ineptness both are nouns.

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

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

inappropriateness: the quality of being not particularly suitable or befitting
ineptness: the quality of having the wrong properties for a specific purpose

Other hypernyms of inappropriateness include unsuitability, unsuitableness.

inappropriateness (noun)	ineptness (noun)
the quality of being not particularly suitable or befitting	the quality of having the wrong properties for a specific purpose
inappropriate conduct	unskillfulness resulting from a lack of training