Pure Marxism is similar to Libertarianism in that there is no government per se. The difference is that a Marxist state first needs a totalitarian system to "reeducate" the people.
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Have you read 'the black book of communism'? I'd say in theroy Marxism is all government because no one owns anything, everything belongs to the state.
libertarianism is different then anarchy in that a vast majority of libertarians believe in the need for some government, or at least an elected force to enforce the basic laws. Libertarians generally believe in at least a partial governmental role at the county or township level, with only loose oversight at the federal level.
In fact, our country was founded on Libertarian principles and remained libertarian until the great depression (or perhaps a bit before WWI).
This isnt taught in public schools.