spinster vs old maid

spinster and old maid both are nouns.

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

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

spinster (noun)	old maid (noun)
an elderly unmarried woman	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')
someone who spins (who twists fibers into threads)	an elderly unmarried woman
	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