The Cold War was an indirect, political, and economic war between the United States and the USSR. No actual battles were fought between the two countries. It was tension and competition to dominate international affairs.
Truman feared the spread of communism. Stalin disliked America's democratic government.
Stalin feared the atomic bomb's creation by the United States. However, the US refused to share nuclear secrets with the USSR.
The USSR disagreed with free trade and capitalism as it introduced western influences, while the US promoted it. This futher separated the two countries.
With the creation of the Truman Doctrine, tension with the USSR grew. Truman announced that any nation that also wanted to prevent the spread of communism was considered an ally. The USSR also continued to impose communism on other contries after agreeing not to do so at the Yalta Conference.