There was no active war between the Soviets and US. Both sides made many attempts to out due each other with power, ideology and allies all over the world.
They were busy arming themselves with nuclear weapons. If the nuclear weapons would have been used it could have destroyed the world.
The United States followed a democratic government which allowed people to freely vote and form political parties. The Soviet Union only had one ruling party and freedom was not provided. This became the root of the Cold War.
The Soviet Union was against free trade, capitalism, and kept its economy from the outside world. The United States promoted the practice of free trade worldwide. Communism and capitalism only widened the gap between the two.
The Truman Doctrine considered any non-communist country and ally to the United States. The atomic bomb was one of the weapons that every country wanted to develop. The Berlin Wall separated East Germany from crossing over to the Western Germany.