city district vs district

city district and district both are nouns.

Word	Noun	Adjective	Verb	Adverb
city district	Yes	No	No	No
district	Yes	No	Yes	No

As nouns, district is a hypernym of city district; that is, district is a word with a broader meaning than city district:

Other hypernyms of city district include dominion, territorial dominion, territory.

city district (noun)	district (noun)
a district of a town or city	a region marked off for administrative or other purposes

city district (verb)	district (verb)
	regulate housing in; of certain areas of towns