peony vs flower

peony and flower both are nouns.

Word	Noun	Adjective	Verb	Adverb
peony	Yes	No	No	No
flower	Yes	No	Yes	No

As nouns, flower is a hypernym of peony; that is, flower is a word with a broader meaning than peony:

peony: any of numerous plants widely cultivated for their showy single or double red or pink or white flowers
flower: a plant cultivated for its blooms or blossoms

peony (noun)	flower (noun)
any of numerous plants widely cultivated for their showy single or double red or pink or white flowers	a plant cultivated for its blooms or blossoms
	reproductive organ of angiosperm plants especially one having showy or colorful parts
	the period of greatest prosperity or productivity

peony (verb)	flower (verb)
	produce or yield flowers