Dictionaries often have different definitions-- particularly for some "political" terminology like "socialism" and "capitalism." It is useless to debate varying dictionary definitions, but the words below will help you see the context of some of the ideas and words at this website so you have an idea what I mean while using these words.

This list is by no means complete.

Libertarian Taxonomy
Left-Libertarian

Capitalism- private and/or monopolistic ownership of the means of production, profit/surplus value, interest, markets, and wage labor (types of capitalists)

Libertarians sometimes debate whether the "real" or "authentic" meaning of a term like "capitalism" is (a) the free market, or (b) government favoritism toward business, or (c) the separation between labor and ownership, an arrangement neutral between the other two; Austrians tend to use the term in the first sense; individualist anarchists in the Tuckerite tradition tend to use it in the second or third. But in ordinary usage, I fear, it actually stands for an amalgamation of incompatible meanings.

Suppose I were to invent a new word, "zaxlebax," and define it as "a metallic sphere, like the Washington Monument." That's the definition — "a metallic sphere, like the Washington Monument. " In short, I build my ill-chosen example into the definition. Now some linguistic subgroup might start using the term "zaxlebax" as though it just meant "metallic sphere," or as though it just meant "something of the same kind as the Washington Monument." And that's fine. But my definition incorporates both, and thus conceals the false assumption that the Washington Monument is a metallic sphere; any attempt to use the term "zaxlebax," meaning what I mean by it, involves the user in this false assumption. That's what Rand means by a package-deal term.

Now I think the word "capitalism," if used with the meaning most people give it, is a package-deal term. By "capitalism" most people mean neither the free market simpliciter nor the prevailing neomercantilist system simpliciter. Rather, what most people mean by "capitalism" is this free-market system that currently prevails in the western world. In short, the term "capitalism" as generally used conceals an assumption that the prevailing system is a free market. And since the prevailing system is in fact one of government favoritism toward business, the ordinary use of the term carries with it the assumption that the free market is government favoritism toward business.

And similar considerations apply to the term "socialism." Most people don't mean by "socialism" anything so precise as state ownership of the means of production; instead they really mean something more like "the opposite of capitalism." Then if "capitalism" is a package-deal term, so is "socialism" — it conveys opposition to the free market, and opposition to neomercantilism, as though these were one and the same.

And that, I suggest, is the function of these terms: to blur the distinction between the free market and neomercantilism. Such confusion prevails because it works to the advantage of the statist establishment: those who want to defend the free market can more easily be seduced into defending neomercantilism, and those who want to combat neomercantilism can more easily be seduced into combating the free market. Either way, the state remains secure.
Roderick Long's Rothbard Memorial Lecture ("Rothbard's 'Left and Right': Forty Years Later")

capitalism vs. capitalism

capitalism: the known reality

distinguished-capitalists

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Libertarianism, Thin- the non-aggression principle (NAP) alone is a sufficient way to answer questions of action-- liberty and life/society. As an aside I don't see why self-ownership alone, without non-agression could also be considered "thin" as it has been argued that NAP is not needed because self-ownership neccessarily leads to non-aggression anyway. One way or the other, it seems the thin approach has Occam in mind.
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Libertarianism, Thick- more than "one" principle is involved in "consitent" libertarianism ..dare I say a 'dialetical' approach to libertarianism
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Libertarianism, One Drop- a single connection to the state is not libertarian (coined by Steve Horwitz?)
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Political economy- analyzing and explaining the ways in which various sorts of government affect the allocation of scarce resources in society through their laws and policies as well as the ways in which the nature of the economic system and the behavior of people acting on their economic interests affects the form of government and the kinds of laws and policies that get made. source 
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Socialism- worker owed production, workers recieve/divide profit/surplus value to recieve their full product, it is not siphoned out of their pockets as in the case of capitalism. Mutualists advocate free-market socialism, collectivist anarchistsworkers cooperatives and salaries based on the amount of time contributed to production, anarcho-communists advocate a direct transition from capitalism to libertarian communism and anarcho-syndicalists worker's direct action and the general strike.
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Vulgar libertarianism- coined by Kevin Carson: "Vulgar libertarian apologists for capitalism use the term "free market" in an equivocal sense: they seem to have trouble remembering, from one moment to the next, whether they’re defending actually existing capitalism or free market principles. So we get the standard boilerplate article in The Freeman arguing that the rich can’t get rich at the expense of the poor, because "that’s not how the free market works"--implicitly assuming that this is a free market. When prodded, they’ll grudgingly admit that the present system is not a free market, and that it includes a lot of state intervention on behalf of the rich. But as soon as they think they can get away with it, they go right back to defending the wealth of existing corporations on the basis of "free market principles."" Kevin Carson Studies in Mutualist Political Economy, p. 142