Past a certain point, there IS no difference between what we have and WW III. Consider WW I, which was not actually called that right away. It was always "The Great War." Then WW II came along and the news wonks needed to differentiate between two distinct wars, each fought on a global level. While the name WW II was used speculatively as early as 1938, it didn't become "official" until Harry Truman signed some document for the Secretary of War in September, 1945 to officially name that conflict WW II. I guess they needed an official designation so they could account for the lost equipment as "expended in combat/WW II" or something like that.