administrative division vs administrative district

administrative division and administrative district both are nouns.

Word	Noun	Adjective	Verb	Adverb
administrative division	Yes	No	No	No
administrative district	Yes	No	No	No

As nouns, administrative division and administrative district are synonyms defined as:

administrative division and administrative district: a district defined for administrative purposes

Other synonyms of administrative division include territorial division.

administrative division (noun)	administrative district (noun)
a district defined for administrative purposes	a district defined for administrative purposes