United States Army vs US Army

United States Army and US Army both are nouns.

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

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

United States Army and US Army: the army of the United States of America; the agency that organizes and trains soldiers for land warfare

Other synonyms of United States Army include Army, U. S. Army, USA.

United States Army (noun)	US Army (noun)
the army of the United States of America; the agency that organizes and trains soldiers for land warfare	the army of the United States of America; the agency that organizes and trains soldiers for land warfare