federal agency vs authority

federal agency and authority both are nouns.

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

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

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

federal 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