The other answers are not quite correct.  Hopefully I will do this subject justice. Konkin’s History of the Libertarian Movement Is an accurate record of libertarianism.  But there are many terms that derive from the root word ‘liberty’ and the preference for liberty.

DEFINITIONS.

LIBERTY: all other things being equal, a preference for private property rights, and the grant of reciprocal freedom from coercion  – of the body, actions and property.

LIBERTARIAN:

  1. Libertarian as an instinctual desire. A biological predisposition in favor of new stimuli expressed as freedom from constraint in obtaining new stimuli.

  2. A moral sentiment: A moral bias giving higher preference to liberty than competing moral sentiments, the most dominant of which are (a) Harm/Care and (b) Loyalty, Respect, Proportionality and Purity.  Left (communalists) is singularly biased toward (a), and right (aristocratic egalitarians) toward (a+b), and libertarians toward (c) Liberty and Proportionality.  Although Proportionality is considered differently by right (paternalistic) and left (maternalistic) factions.

  3. Libertarian as a Political Preference: A preference for the least government intervention in the economy as possible.  There are many thinkers and groups that fall into this category, including most conservatives, as well as classical liberals. The point of demarcation between social conservatives (conservatism) and economic conservatives (libertarians) is whether it is necessary to enforce norms by threat of law, or (as libertarians argue) the market is a sufficient means of enforcing normative ethics.)  

BTW: Libertarians are empirically wrong on this subject, and conservatives simply lack a means of articulating the conditions under which it is permissible to altern norms – such as homosexuality, now that we know it is a biological factor not a choice. They  have no exit, even if they would adapt if they could.  So the libertarian and conservative groups remain divided. (Which I am admittedly trying to change.)

Furthermore, the right uses an ancient, well-known and well-understood tactic of rebellion against oppression: religion, and the use of metahorical rather than secular rational language. It is the same religion that the simple people used to resist roman norms and culture while finding community in the newly mobile mediterranean world created by Rome.  It is the same technique used by the germans to free themselves from mediterranean trade, tax, government and morals.

This is also the strategy in use by the Religion of Postmodernism and the institution of the Democratic Socialist State. Having demonized mystical religion in favor of the religion of ‘scientific socialism’, when Communism and Socialism were demonstrated to be failures in both theory and practice it  became necessary to resort to Chomskyian ‘framing’ in order to replace religious mysticism with contra-rational falsehoods and contra-factual impossibilities that can be constantly repeatedin contradictory contexts thereby creating an alternate reality of non-rational but contextual associations by way of chanting – just as islam does through daily repetition, christianity and judaism do through rituals and prayer.

All religous systems bring people into groups to evoke the sense of spirituality, which is our pre-human desire to surrender our minds and wills to the elation of the running pack (yes, that is what spirituality is caused by),  and then to repeat mantras and narratives in this circumstance. 

Tribal peoples in the tropical belt do the same thing by chanting and dancing – its’ all the same process.

Western heroicism was accomplished by repeating some variation of either the prehistoric Indo-european, Homeric, Roman, Carolingian, or Arthurian legends around the feast’s fire pits. Americans repeated the narrative of the Cult of the Revolution around hearths, churches and schools, and in books, pamphlets and speeches.

It is the same process in every human society. It works. We evolved to run down game together. That is why we look different from apes, and act like wolves. We are very efficient at running and dissipating heat. We can run down any animal on earth. We do not have to fight them. Just chase them as a pack until they are exhausted.  Watch a video of Masai crossing a plain. That is human biological advantage.

The process of repeating ideas within a context allows us to create intuitive associations and therefore intuitive responses, instead of depending upon our demonstrably frail reason.  It is our pre-rational system of learning. We use it still today.

And because nearly all of our decisions are made intuitively. So these intuitions end up with greater expression than those of our reason.  In the case of postmodernism (progressivism), and christianity  (social conservatism), these narratives are irrational by false logic and fact (progressivism) or arational by mystical allegory (conservatism).

  1. Libertarianism as a Political Philosophy:
    As articulated by Rothbard, libertarianism it is a rigorous, analytically stated ethical and political philosophy originating with natural law. The ethical system is based on very smple rules: your body and those things that you obtain by voluntary exchange, are yours, and you have a monopoly on the use of them. Don’t steal, dont commit fraud, and don’t initiate violence, and you have respected the same of others.

The state is a corporation of shareholders who we call bureaucrats, who extract unwilling fees from hard working people, in order to fund their own indolence rather than do the equally hard work of taking risks in the market. Norms are unnecessary because the market for competition and reputation will instill the proper commercial normative respect for property without the intervention of a government (something privately owned), or a state(something abstractly owned).

Libertarianism was designed to create an opposition religion to the marxist, socialist, and postmodernist religions. It is an ideological system based upon the jewish rebellious ethic of the ghetto. The primary content of this ethical system is a very limited concept of  property rights, where those property rights are absent the prohibitions on involuntary transfer by asymmetry and externality, that are necessary to fund investments in the commons of high trust norms.  It is the ethics of the low trust society. This is why it is a demonstrated failure outside of a narrow niche of americans.  Because the rest of americans, while they cannot articulate these ideas in rational terms, correctly intuit that rothbardian libertarianism is immoral.  Because it is. It is a means of rebellion. It is a religion.  And its ethics are immoral. 

  1. Libertarianism as a Political Ideology : Having observed the methodology of Marxists in propagating ideas,  Libertarianism has been promoted by the Mises institute into an ideology. An ideology is a set of memes that attempt to obtain power for a body of people in a political system.  Ideology is  different from philosophy in that the larger community relies upon representatives (intellectuals, priests, symbolic individuals) and argues by analogy, rather than making use of the precise arguments of their philosophy, if they oculd rationally master and articulate it.   That these short narratives are the equivlaent of mythic narratives is not material since the purpose is to motivate people emotionally to action, not intellectually to agreement. If you understand this then you will understand the purpose of most political ideology: motivation to act.

ANARCHO-CAPITALISM
6) Anarcho-capitalist branch of libertarianism:  Anarcho Capitalism is one of a number of monikers representing different factoins within the libertarian political, moral, sentimental movements.  This moniker was necessary in order to distinguish those followers of rothbard and mises, from those who also used the term libertarian, and had other rationales and arguments – and leadership.

Anarcho-Capitalism is a more specific, and very thoroughly articulated, extension of libertarian philosophy to include the works of additional thinkers, the most important of which is Hans Hoppe. Hoppe’s insight was technical: that we could solve the problem of the natural behavior of monopolistic bureaucracies by replacing mandatory bureaucracies with private insurance companies, provide for defense, justice, and policing with private organizations.  Since there is only one ‘law’ in anarcho capitalism – private property – then the constitution doesn’t need to be written, or modified.  Intellectuals (myself included) consider Anarcho Capitalism one of the most interesting and successful political research programs.  Others treat it like an exetension of libertarian philosophy, and others practice it as an ideology.  But this is a description of the different rhetorical abilities of practitioners and little else.

https://www.quora.com/Is-libertarianism-the-same-as-anarcho-capitalism