billiard room vs billiard parlour

billiard room and billiard parlour both are nouns.

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

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

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

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