The term cold war refers to the conflict (heightened tension) that existed for almost 50 years between the united states and what other country?

The Union of Soviet Socialist Republics (USSR).

Some of the deeper issues that set the USA and the USSR at odds were that the USA was committed to capitalism and democratic institutions of government, whereas the USSR was committed to communism and imposed authoritarian government.  The Cold War was mostly a tension between these worldviews.
There were also immediate conflicts and pressure points as the Cold War began. One of those issues was that the USA had atomic weapons and the USSR did not.  (The US would not share that technology with the Soviets, who had been their ally in World War II.)  When the Soviets developed their own atomic weaponry, this led to a massive arms race between the superpowers.