Which two ideologies were involved in a conflict during the Cold War era?

Communism and Capitalism

The Cold War was not simply a matter of power rivalries, of military alliances, and of the balance of power. These were accompanied by a real ideological conflict as well, a difference over the best and the most appropriate way of organising political, economic, and social life all over the world. The western alliance, headed by the US, represented the ideology of liberal democracy and capitalism while the eastern alliance, headed by the Soviet Union, was committed to the ideology of socialism and communism.