The Korean war was authorized by President Truman, and it led to the beginning of a new era of U.S. policy of containment. It was a political war that pitted the U.S. against the Soviet Union. The question of which side won is debatable when it is viewed through the lens of political and military reasons. According to Stewart (2005), the war devastated Korea and created a platform where the U.S. was able to expand its military presence around the world. However, the quick answer to who won the war should be that it ended in a stalemate, or as many scholars would say, it frustrated many on either side and ended in an armistice. America would only define victory from the war as the ensuing expansion of its military presence and expansion around the world.
Despite the high level of casualties experienced during the war from both sides, I would define victory as the prevention of a war between the U.S., Russia, and China that could have probably resulted into the Third World War. The war could have been much worse had it escalated even though there was still a recorded heavy casualty by the time the war ended in 1953. This was an important development in the U.S. history because the containment policy set in that would prevent the eruption of a full-scale war which would have been disastrous given the presence of nuclear weapons. The short-term goal was that the U.S. was able to oversee the removal of the Japanese colonial government as well as repatriate military personnel to Japan. However, President Truman was not favored by the war as he was judged to have failed to resolve it promptly.
Stewart, R. W. (2005). American Military History: The United States Army in a Global Era, 1917-2003. Government Printing Office.
Stueck, W. (2013). Rethinking the Korean War: A New Diplomatic and Strategic History. Princeton University Press.