When was the war between Russia and the US?

The war between USA and USSR( Now Russia) happened a few years later after World War II. They're the 2 strongest nations in the world. It was caused by disagreements with the 2 countries. The USA believes in freedom & big business. The USSR is communist. It was called the Cold war. After the Cold war, they made a space competition to get to the moon. USSR launched their rocket first but USA made it towards the moon.