Some forms of libertarians, especially in the US, overlap almost to being identical with anarcho-capitalists, which is a type of anarchism. Libertarian can mean a lot of different things depending on the person, but few of them seem appropriate for government office.
Anarchism is synonymous with libertarian socialism. They are Marxists and seek to abolish capitalism.
In the mid-20th century, right-libertarian proponents of anarcho-capitalism and minarchism co-opted the term libertarian to advocate laissez-faire capitalism and strong private property rights such as in land, infrastructure and natural resources. The latter is the dominant form of libertarianism in the United States, where it advocates civil liberties, natural law, free-market capitalism and a major reversal of the modern welfare state.[1]