We don't have synonyms for american war yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are american way, mexican war and american star.
(n) :
(military, history) In English language usage, any of several wars involving the United States of America, in non-U.S. local contexts.
(n) :
(In Vietnam, when speaking English) Vietnam-American War/American-Vietnam War, known as the Vietnam War outside of Vietnam in the English speaking world.
(n) :
(UK, obsolete) The American Revolutionary War, American War of Independence
(n) :
(military, history) In English language usage, any of several wars involving the United States of America, in non-U.S. local contexts.
(n) :
(In Vietnam, when speaking English) Vietnam-American War/American-Vietnam War, known as the Vietnam War outside of Vietnam in the English speaking world.
(n) :
(UK, obsolete) The American Revolutionary War, American War of Independence