billiard hall vs billiard parlour

billiard hall and billiard parlour both are nouns.

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

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

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

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