border district vs territory

border district and territory both are nouns.

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

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

border district: district consisting of the area on either side of a border or boundary of a country or an area
territory: a region marked off for administrative or other purposes

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

border district (noun)	territory (noun)
district consisting of the area on either side of a border or boundary of a country or an area	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