The definitions were formatted so that people could figure out where they fit in based on their political beliefs.
The "US definition" qualifier is used because while we tend to identify Conservative with the right and Liberal with the left, and that is often not the case in most other places. We had to pick one in order to have some kind of base point, and, since most here are Americans, that's what we went with. But the definitions are worded and examples of non-American groups are given so that people who might use a different term to describe the same thing can find out where they belong.
Libertarianism, Socialism, and Capitalism are different animals. Where "liberal" and conservative" are typically used to describe a political position, these three are established political and/or economic philosophies with well established definitions that are generally accepted everywhere. While individual schools do exist within each that can vary greatly in their specific teachings, the core ideas remain the same. A libertarian is going to advocate for freedom above all else, a socialist is going to advocate for social ownership and cooperation, and a capitalist is going to advocate for a for-profit economy.