mess hall vs dining room

mess hall and dining room both are nouns.

Word	Noun	Adjective	Verb	Adverb
mess hall	Yes	No	No	No
dining room	Yes	No	No	No

As nouns, dining room is a hypernym of mess hall; that is, dining room is a word with a broader meaning than mess hall:

mess hall: a (large) military dining room where service personnel eat or relax
dining room: a room used for dining

Other hypernyms of mess hall include dining-room.

mess hall (noun)	dining room (noun)
a (large) military dining room where service personnel eat or relax	a room used for dining