federal agency vs government agency

federal agency and government agency both are nouns.

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

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

federal agency and government agency: an administrative unit of government

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

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