office vs federal agency

office and federal agency both are nouns.

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

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

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

office (noun)	federal agency (noun)
a religious rite or service prescribed by ecclesiastical authorities	an administrative unit of government
the actions and activities assigned to or required or expected of a person or group
a job in an organization
place of business where professional or clerical duties are performed
professional or clerical workers in an office
an administrative unit of government
(of a government or government official) holding an office means being in power