The fundamental disagreement was over which superpower would control post WWII Europe. The Soviets had control over Poland and the Balkans. The American and British forces liberated western European areas from Scandinavia down to Italy. Russia had goals of establishing communist governments, which were loyal to the Soviet Union. The United States held the principle of democracy and insisted that people chose their post war rulers freely. (Divine, 810)
In the late 40's through early 50's the Soviet Union started to spread the Lenin ideological as it started moving in the western block in Europe. The US started funding the rebuilding of European infrastructure in a system called the Marshall Plan. Marshall appointed Dean Acheson as his undersecretary of state, and George Keenan to head the new Policy Planning Staff. These two individuals played a very important role in creating the foreign policy of the United States for the next several decades, especially when it related to Russia and the U.S.'s attempts to contain it.
The Truman Doctrine comes from a speech given by President Truman to Congress on March 12, 1947, asking for 400 million in military and economic aid for Greece. The worry was that the communists in Greece were being supported by the Russians and if Greece fell to the communists in its civil war, communism would spread throughout the Mediterranean. This Doctrine puts forth the idea that by affecting a country other than Russia we are still fighting the Russians by proxy. (Divine, 813) "It must be the policy of the United States," Truman told Congress, "to support free peoples who are resisting attempted subjugation by armed minorities or by outside pressure." (Divine, 813) This Doctrine marked the beginning of the Cold War between the United States and Russia.
The policy of containment issued by Secretary of State, General George C. Marshall, and created by Keenan and Acheson was first implemented by President Truman in aiding Greece against its communist insurrection. This policy of fighting the Russians by Proxy was the key concept of the Truman Doctrine and the result of the containment policy created by Marshall, Keenan, and Acheson. This led to several major engagements in backwaters of Asia for the United States, from Korea to Vietnam. These and many smaller engagements were a direct result of the containment policy and the adoption of the Truman Doctrine.
Russia in turn brought forth its own funding called the Molotov Plan. Because of that, they were able to spread communism through many countries. Some of these nations were: Poland, Romania, Bulgaria, Hungary, Czechoslovakia, Eastern Germany, and numerous countries in Southeastern Asia. But on the US side we had the support from almost the entire Western Europe. So the tension started, between Western Europe or a republic society and Eastern Europe and communism. (Divine, 817)