department of the federal government vs federal office

department of the federal government and federal office both are nouns.

Word	Noun	Adjective	Verb	Adverb
department of the federal government	Yes	No	No	No
federal office	Yes	No	No	No

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

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

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

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