old maid vs spinster

old maid and spinster both are nouns.

Word	Noun	Adjective	Verb	Adverb
old maid	Yes	No	No	No
spinster	Yes	No	No	No

As nouns, old maid and spinster are synonyms defined as:

old maid (noun)	spinster (noun)
a card game using a pack of cards from which one queen has been removed; players match cards and the player holding the unmatched queen at the end of the game is the loser (or `old maid')	an elderly unmarried woman
an elderly unmarried woman	someone who spins (who twists fibers into threads)
the loser in a game of old maid
commonly cultivated Old World woody herb having large pinkish to red flowers
any of various plants of the genus Zinnia cultivated for their variously and brightly colored flower heads