Anarchism (as in libertarian-socialism or socialist-libertarianism) is left-wing because it stands for a free society both economically and socially.
The party you are talking about is probably Anarcho-capitalist (mostly referred to as Libertarianism). They do not want social-freedom, just economic-freedom.
So where left-wing anarchists want to abolish capitalism, (most) libertarian-parties do not.
Look at this chart:
The left is (how surprising) to the left. Right is capitalism, left is communism.
Important here is the y-axis. It represents "libertarian" and "authoritarian".
Fascism would be in the right-bottom corner, Stalinism in the left-bottom corner (i'll be probably strung up by supporters for this, but hey).
The left-wing anarchists are in the top-left corner and the libertarians you are talking about are in the top-right corner.
So, to sum up: there is a difference between libertarians and libertarians.



