quarters vs housing

quarters and housing both are nouns.

Word	Noun	Adjective	Verb	Adverb
quarters	Yes	No	No	No
housing	Yes	No	No	No

As nouns, housing is a hypernym of quarters; that is, housing is a word with a broader meaning than quarters:

Other hypernyms of quarters include living accommodations, lodging.

quarters (noun)	housing (noun)
housing available for people to live in	structures collectively in which people are housed
	a protective cover designed to contain or support a mechanical component
	stable gear consisting of a decorated covering for a horse, especially (formerly) for a warhorse