residence hall vs quarters

residence hall and quarters both are nouns.

Word	Noun	Adjective	Verb	Adverb
residence hall	Yes	No	No	No
quarters	Yes	No	No	No

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

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

Other hypernyms of residence hall include building, edifice, living quarters.

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