Is Libertarian related to Liberal or Liberalism?
Only by the root of the word which is "liber" meaning free. The similarities break apart when you look at modern political philosophies. Liberals are open to free expression and social ideals, but fall short when going into economic freedoms which are just as important. Libertarians apply the idea of freedom equally across the full spectrum of social and governmental ideas.
So the Libertarian party is is own seperate and distrinct set of principles that make it stand out in comparison despite the similar root in the name. So next time you see (Lib) on a ballot it means Libertarian and not liberal.