department of the federal government vs federal department

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

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

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

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

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

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