The history of mistrust between the Soviet Union and the US began in 1919, when WWI allies (Britain and US) helped the White Army (anti-Bolsheviks) fight against the Bolsheviks during Russia's civil war. When the Bolshevik's won and rose to power, they never again trusted the West. In return, the US also had long been concerned about the Soviet Union's views on socialism and communism.
This mutual tension was evident in WWII when both countries were uneasy allies. For example, the Soviet Union was excluded from the US/Britain creation of the atomic bomb. Also, Russia asked the allies for a second front, but was offended when they had to wait longer than they expected. Stalin believed this was done on purpose to weaken Russian forces.
After WWII, Roosevelt and Churchill had contrasting visions of the world. Roosevelt's global goals included the US economy dominating over the British Empire. This led to both having separate dealings with the Soviets. However, the situation became more complicated with the Cold War.