government agency vs authority

government agency and authority both are nouns.

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

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

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

government agency (noun)	authority (noun)
an administrative unit of government	the power or right to give orders or make decisions
	official permission or approval
	freedom from doubt; belief in yourself and your abilities
	an authoritative written work
	an administrative unit of government
	an expert whose views are taken as definitive
	(usually plural) persons who exercise (administrative) control over others