State Department vs Department of State

State Department and Department of State both are nouns.

Word	Noun	Adjective	Verb	Adverb
State Department	Yes	No	No	No
Department of State	Yes	No	No	No

As nouns, State Department and Department of State are synonyms defined as:

State Department and Department of State: the federal department in the United States that sets and maintains foreign policies

Other synonyms of State Department include DoS, State, United States Department of State.

State Department (noun)	Department of State (noun)
the federal department in the United States that sets and maintains foreign policies	the federal department in the United States that sets and maintains foreign policies
a department of government in one of the 50 states