parlor vs common room

parlor and common room both are nouns.

Word	Noun	Adjective	Verb	Adverb
parlor	Yes	No	No	No
common room	Yes	No	No	No

As nouns, common room is a hyponym of parlor; that is, common room is a word with a more specific, narrower meaning than parlor:

parlor: a room in a private house or establishment where people can sit and talk and relax
common room: a sitting room (usually at school or university)

Other hyponyms of parlor include morning room, salon.

parlor (noun)	common room (noun)
reception room in an inn or club where visitors can be received	a sitting room (usually at school or university)
a room in a private house or establishment where people can sit and talk and relax