residential district vs residential area

residential district and residential area both are nouns.

Word	Noun	Adjective	Verb	Adverb
residential district	Yes	No	No	No
residential area	Yes	No	No	No

As nouns, residential district and residential area are synonyms defined as:

residential district and residential area: a district where people live; occupied primarily by private residences

Other synonyms of residential district include community.

residential district (noun)	residential area (noun)
a district where people live; occupied primarily by private residences	a district where people live; occupied primarily by private residences