US Navy vs United States Navy

US Navy and United States Navy both are nouns.

Word	Noun	Adjective	Verb	Adverb
US Navy	Yes	No	No	No
United States Navy	Yes	No	No	No

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

US Navy and United States Navy: the navy of the United States of America; the agency that maintains and trains and equips combat-ready naval forces

Other synonyms of US Navy include Navy, USN.

US Navy (noun)	United States Navy (noun)
the navy of the United States of America; the agency that maintains and trains and equips combat-ready naval forces	the navy of the United States of America; the agency that maintains and trains and equips combat-ready naval forces