federal department vs federal office

federal department and federal office both are nouns.

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

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

federal department and federal office: a department of the federal government of the United States

Other synonyms of federal department include department of the federal government.

federal department (noun)	federal office (noun)
a department of the federal government of the United States	a department of the federal government of the United States