city district vs territory

city district and territory both are nouns.

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

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

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

city district (noun)	territory (noun)
a district of a town or city	an area of knowledge or interest
	a region marked off for administrative or other purposes
	the geographical area under the jurisdiction of a sovereign state