parterre vs flower garden

parterre and flower garden both are nouns.

Word	Noun	Adjective	Verb	Adverb
parterre	Yes	No	No	No
flower garden	Yes	No	No	No

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

parterre: an ornamental flower garden; beds and paths are arranged to form a pattern
flower garden: a garden featuring flowering plants

parterre (noun)	flower garden (noun)
seating at the rear of the main floor (beneath the balconies)	a garden featuring flowering plants
an ornamental flower garden; beds and paths are arranged to form a pattern