I've done some more reading, and some people have referred to the Cold War as "WW III" and the GWOT as "WW IV"
The Cold War was fought by the U.S. and the USSR/Warsaw Pact (mainly by proxy) in Asia, Africa, and Central America. There were a fair number of non shooting confrontations (between the US and USSR) in Europe as well. The Soviets didn't hesitate in shooting Hungarians in 1956 or Czechs in 1968.
The U.S. and Allies have fought the GWOT in North America, Europe, Africa, and Asia.