government agency vs federal agency

government agency and federal agency both are nouns.

Word	Noun	Adjective	Verb	Adverb
government agency	Yes	No	No	No
federal agency	Yes	No	No	No

As nouns, government agency and federal agency are synonyms defined as:

government agency and federal agency: an administrative unit of government

Other synonyms of government agency include agency, authority, bureau, office.

government agency (noun)	federal agency (noun)
an administrative unit of government	an administrative unit of government