dorm vs quarters

dorm and quarters both are nouns.

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

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

dorm: a college or university building containing living quarters for students
quarters: housing available for people to live in

Other hypernyms of dorm include building, edifice, living quarters.

dorm (noun)	quarters (noun)
a college or university building containing living quarters for students	housing available for people to live in