The Cold War was a great power contest that had many dimensions. There was a "war of ideas," and there were military confrontations. But there were also proxy wars, vast alliances, and institutions for managing the conflict -- indeed, it was a highly formalized affair, with mechanisms, treaties, ambassadors, and so on specifically dedicated to defusing potential conflict. It was, most important, an inter-state competition. The states could and did speak with each other, negotiate with each other, trade with each other, sustain cultural and educational exchanges, and the like, for decades.
While the causes of the end of the Cold War remain a contentious topic, there is much to suggest that these dense networks, institutions, global norms, rational discourse, and civil society advocacy had enormously powerful effects in lowering tensions and opening opportunities to conclude the rivalry. The military competition was essentially a stalemate. Up to the end, American hardliners warned of Soviet nuclear superiority, for example, or their numerical advantages in the European theater. And the major proxy war -- Vietnam -- was a colossal failure for the United States.
The Cold War was ended by engagement, rather than "destroying the threat," and that is a powerful lesson. But because of the highly formal and state-centric nature of the confrontation, one has to ask if there is any relevance to the "twilight struggle" with Soviet communism.