Libertarianism is a big tent. There are right-libertarians (like the ones you describe), left-libertarians, anarchist-leaning libertarians, Randian Objectivists

Libertarianism is a big tent. There are right-libertarians (like the ones you describe), left-libertarians, anarchist-leaning libertarians, Randian Objectivists, etc. These camps differ in numerous ways but there's a general undercurrent and large areas of agreement.