US Government vs United States government

US Government and United States government both are nouns.

Word	Noun	Adjective	Verb	Adverb
US Government	Yes	No	No	No
United States government	Yes	No	No	No

As nouns, US Government and United States government are synonyms defined as:

US Government and United States government: the executive and legislative and judicial branches of the federal government of the United States

Other synonyms of US Government include U.S., U.S. government, United States.

US Government (noun)	United States government (noun)
the executive and legislative and judicial branches of the federal government of the United States	the executive and legislative and judicial branches of the federal government of the United States