cohabitation vs inhabitancy

cohabitation and inhabitancy both are nouns.

Word	Noun	Adjective	Verb	Adverb
cohabitation	Yes	No	No	No
inhabitancy	Yes	No	No	No

As nouns, inhabitancy is a hypernym of cohabitation; that is, inhabitancy is a word with a broader meaning than cohabitation:

cohabitation: the act of living together and having a sexual relationship (especially without being married)
inhabitancy: the act of dwelling in or living permanently in a place (said of both animals and men)

Other hypernyms of cohabitation include habitation, inhabitation.

cohabitation (noun)	inhabitancy (noun)
the act of living together and having a sexual relationship (especially without being married)	the act of dwelling in or living permanently in a place (said of both animals and men)