One of the greatest differences is that South Korea emphasizes the group more than the individual. In America, we often emphasize the individual at the expense of the group.
Korea is also very homogeneous, although Seoul is becoming a more international city. It is for good reason that South Korea is called the hermit kingdom. America, by contrast, at least in the major cities, is more international.
Korea is an ancient country that dates back thousands of years. America is a new country with a relatively short history. In light of this, Korea is much more traditional than America. Finally, Korean honor their elders much more than in America, as it is rooted in the philosophy of Confucius.
There are many differences between South korea and America. One difference is there is a large family system in South Korea, but people support themselves system in America. There is a restricted life style in South Korea, but a free life style in America. American also has a variation in cultures as compared to South Korea. In South Korea there is a group mind set but individual mind set in America. Another difference is a lower cost or standard of living in South Korea. An important difference is safer because most people can't have guns, but in America many people can own guns.