authority vs federal agency

authority and federal agency both are nouns.

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

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

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

authority (noun)	federal agency (noun)
the power or right to give orders or make decisions	an administrative unit of government
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