Most branches of Marxism want to use the state to impose social change. This change is usually referred to as top-down change.

Anarchists, on the other hand, do not want to use the state or any sort of top-down command in order to create change. Anarchists want bottom-up change. They differ on specifics, but anarchists want to use trade unions, neighborhood assemblies, collectives, cooperatives and grassroots organization in general to create social change.

By the way, I hope you know that "libertarian" for most of history was a synonym for anarchism. It was only in the past 30-40 years that American proprietarians underwent a huge propaganda campaign to call their philosophy "libertarianism."

Read this for more info, just so you know:

http://theanarchistlibrary.org/HTML/The_Anarchist_FAQ_Editorial_Collective__150_years_of_Libertarian.html

As is well known, anarchists use the terms “libertarian”, “libertarian socialist” and “libertarian communist” as equivalent to “anarchist” and, similarly, “libertarian socialism” or “libertarian communism” as an alternative for “anarchism.” This is perfectly understandable, as the anarchist goal is freedom, liberty, and the ending of all hierarchical and authoritarian institutions and social relations.

Unfortunately, in the United States the term “libertarian” has become, since the 1970s, associated with the right-wing, i.e., supporters of “free-market” capitalism. That defenders of the hierarchy associated with private property seek to associate the term “libertarian” for their authoritarian system is both unfortunate and somewhat unbelievable to any genuine libertarian. Equally unfortunately, thanks to the power of money and the relative small size of the anarchist movement in America, this appropriation of the term has become, to a large extent, the default meaning there. Somewhat ironically, this results in some right-wing “libertarians” complaining that we genuine libertarians have “stolen” their name in order to associate our socialist ideas with it!

The facts are somewhat different. As Murray Bookchin noted, “libertarian” was “a term created by nineteenth-century European anarchists, not by contemporary American right-wing proprietarians.” [The Ecology of Freedom, p. 57] While we discuss this issue in An Anarchist FAQ in a few places (most obviously, section A.1.3) it is useful on the 150^th anniversary to discuss the history of anarchist use of the word “libertarian” to describe our ideas.

The first anarchist journal to use the term “libertarian” was La Libertaire, Journal du Mouvement Social. Somewhat ironically, given recent developments in America, it was published in New York between 1858 and 1861 by French communist-anarchist Joseph Déjacque. The next recorded use of the term was in Europe, when “libertarian communism” was used at a French regional anarchist Congress at Le Havre (16–22 November, 1880). January the following year saw a French manifesto issued on “Libertarian or Anarchist Communism.” Finally, 1895 saw leading anarchists Sébastien Faure and Louise Michel publish La Libertaire in France. [Max Nettlau, A Short History of Anarchism, pp. 75–6, p. 145 and p. 162]