billiard saloon vs billiard hall

billiard saloon and billiard hall both are nouns.

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

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

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

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