residential area vs residential district

residential area and residential district both are nouns.

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

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

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

Other synonyms of residential area include community.

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