In what ways did the histories of the two superpowers affect their outlooks and fears about the postwar world?
There were two major contributing factors to the diverging positions of the United States and Soviet Union after World War II.
The first was the war itself. With the exception of one fairly minor incursion at Pearl Harbor, located outside the continental United States, the position of the United States was one of security and prosperity. The war was being fought on foreign soil and the United States infrastructure benefited from the war rather than being damaged. The Soviet Union had been invaded by Hitler and was deeply suspicious that the Allies were not as supportive on the eastern as on the western front. This led to an attitude of fairly justifiable paranoia. That the US was the only country to ever actually use an atomic bomb in a war also worried the USSR.
The United States, on the other hand, was well on its way to becoming the world's economic and military hyperpower, and benefited from an influx of scientists and other well educated and prosperous foreigners fleeing the devastation of Europe, leading to a general attitude of optimism.