War of American Independence vs American War of Independence

War of American Independence and American War of Independence both are nouns.

Word	Noun	Adjective	Verb	Adverb
War of American Independence	Yes	No	No	No
American War of Independence	Yes	No	No	No

As nouns, War of American Independence and American War of Independence are synonyms defined as:

War of American Independence and American War of Independence: the revolution of the American Colonies against Great Britain; 1775-1783

Other synonyms of War of American Independence include American Revolution, American Revolutionary War.

War of American Independence (noun)	American War of Independence (noun)
the revolution of the American Colonies against Great Britain; 1775-1783	the revolution of the American Colonies against Great Britain; 1775-1783