It is very hard to say that the US has changed the way it relates to all other countries in the same way over the last 20 years. Instead, it seems more appropriate to say that relations with different countries have changed in different ways.
The relationship with China has changed because China has grown more powerful. With the end of the Cold War, geopolitical military issues have become less important and economic issues have taken on greater importance. China's rise has created a host of issues for the US. It has to deal with China as an important economic power even as it is in conflict with China over issues such as Taiwan, Tibet, and the value of the Chinese currency.
In many cases, including that of China, America's dealings with other countries have come to revolve around economics more than around military issues.