How does that whole package of thought (ideological understanding) translate to other later threats?
A whole empire of ideological understanding was built around the interpretive concept of the Cold War and containment of the Communist global threat to world peace as known in the Western democracies.
I think that a good argument can be made that the ideological understanding of the Cold War does not translate to other later threats. For example, the interpretive concept of the Cold War was fundamentally challenged by the world that followed the Cold War. The Cold War essentially froze the geopolitical scale around the world, focusing on the Americans and the Soviets. The Cold War was, interestingly enough, one of the most peaceful periods in Europe and around the world. Outside of situations such as Vietnam and Afghanistan, the Cold War created a binary opposition in which most of the world's political interests were locked.
This concept was fundamentally altered in the world that followed the end of the Cold War. Containment could not as easily be applied to the raging civil wars that took place once the Soviet Union was disbanded. Similar to lifting up the proverbial rock and not liking what lies underneath, the multipolarity condition of the world was something that went against the concept of the Cold War. America found itself fundamentally challenged in trying to embrace the paradigm shift. "The enemy" was not one force. "The enemy" was all over and their agendas were vastly different than the singular focus presented in the Cold War.
The idea of the Western democracy standing for world peace and being perceived as such a force became transformed by the War on Terror. The current engagement with "the enemy" is about as far removed from the Cold War as one can get. In this 21st Century model of war fighting, there is no "nation" that is the "enemy." The threat is borderless, sometimes without army, and can strike at any time with a good internet connection and a disposable, traceless cell phone. Even though President Bush sought to draw a Cold War parallel with the War on Terror, the reality is that it challenges the interpretive concept that was previously understood during the standoff with the Soviet Union:
"The cold war is a good template to begin to think about how to deal with the challenge of radical Islam," says Andrew Bacevich, a former Army colonel and now professor of international relations at Boston University. "The problem is that whatever the president is saying now, his administration's policies have not mirrored the policies of the cold war – starting with the fact that US strategy in the cold war was not primarily oriented towards an aggressive use of force."
The stateless notion and the formal condition of the interpretive notion of the Cold War is challenged with the War on Terror. I think that this is where the paradigm of the Cold War proves to have been a limiting function.