FAA vs government agency

FAA and government agency both are nouns.

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

As nouns, government agency is a hypernym of FAA; that is, government agency is a word with a broader meaning than FAA:

FAA: an agency in the Department of Transportation that is responsible for the safety of civilian aviation
government agency: an administrative unit of government

Other hypernyms of FAA include agency, authority, bureau, federal agency, office.

FAA (noun)	government agency (noun)
an agency in the Department of Transportation that is responsible for the safety of civilian aviation	an administrative unit of government