billiard hall vs billiard room

billiard hall and billiard room both are nouns.

Word	Noun	Adjective	Verb	Adverb
billiard hall	Yes	No	No	No
billiard room	Yes	No	No	No

As nouns, billiard hall and billiard room are synonyms defined as:

Other synonyms of billiard hall include billiard parlor, billiard parlour, billiard saloon.

billiard hall (noun)	billiard room (noun)
a room in which billiards is played	a room in which billiards is played