I would argue that the entire 20th century was in effect, one long continuous war, starting in 1914 with the collapse of the old European order, followed by a 20-year armistace, followed by the six-year hell of "WW II," which was then follwed by the 50-year Cold War. In each case, the renewed hostilities grew out of unresolved issues from the previous ones. At root, it pitted authoritarian/totalitarian political systems against self-determining democracies and republics. Freedom triumphed, but at enormous costs, both economic and social. I would appropriate the term "Great War", now used to refer solely to the first 4 years of it, and apply it to the entirety of that titanic struggle.
The new "War on Terror," although pre-saged by other incidents, started on September 11, 2001 and is somewhat different; it largely grew out of the establishment of the state of Israel in 1947 and reflects the Islamic Third World's resentment of their inferior economic and cultural status. It is a wholly new and different type of war, so much so that many supposedly intelligent commentators actually question whether it's a war at all.
I would argue your earlier premise, that the current war is an outgrowth of the previous war. The Cold War (or WW III, as some of us like to call it) produced Vietnam, which gave a rise to radical liberalism, which fostered energy policies that prevented domestic exploitation of our own resources. This liberalism also was responsible for a "hands off" approach when Islamunists appropriated our resources by nationalizing American oil companies properties overseas.
In short, if we'd have kicked butt quickly in Nam, we would have been able to have the national will to kick Arab butt, and we wouldn't have ragheads with riches to contend with. Also, we funded some pretty unsavory characters in that part of the world in order to beat the Soviets, and that's coming back to bite us in the arse today. Clearly, the Islamofacists see our handling of Vietnam to be their blueprint for victory today.