It appears there are as many liberalisms as there are liberals. To name just a few: libertarianism, classical liberalism, bleeding heart liberalism, economic liberalism, political liberalism, social liberalism, high liberalism, minarchism, objectivism, anarcho-capitalism, neoliberalism. And in international relations theory there is for example neoliberal institutionalism, liberal internationalism or embedded liberalism. Clearly this all amounts to a liberal mess. I attempt to sort it out in my forthcoming book Degrees of Freedom. Political Philosophy and Ideology (Transaction Publishers, April 2015).
Getting a decent grasp of liberal political thought does not have to be this complicated. You only need to keep in mind a perennial question in political philosophy: what is the just relation between the state and the individual? Roughly, there are three answers: the state should have (almost) no role in individual life, the state should have a limited role, or the state should have a fairly large role. The liberal variants that are associated with these answers are libertarianism, classical liberalism and social liberalism, respectively. To be sure, these three are not completely mutually exclusive, while the thinkers associated with these do not always neatly fit the categorization.
This is not the right place to discuss the methodological underpinnings in detail. Suffice it to note that the divide is based on the analysis and ranking of the main political concepts in classical liberalism, social liberalism and libertarianism. This method originates in the writings of British political theorist Michael Freeden. Put briefly, every political ideology should be seen as a framework made of a number political concepts, who vary in importance. Accordingly, all three liberal variants have core, adjacent and peripheral concepts. Sometimes the individual concepts overlap, but in total there is significant variation, leading to the three liberal variants.
Classical liberalism originates from the eighteenth century Scottish Enlightenment, not least in in the writings of David Hume and Adam Smith. It is also associated with thinkers such as Ludwig von Mises, Friedrich Hayek, Milton Friedman and James Buchanan. It has a realistic view of human nature, which means that man is seen a mix between rationality and emotion. Individual freedom is the main classical liberal goal, which is best preserved by protection of classical human rights (freedom from), the rule of law in public affairs and reliance on spontaneous ordering processes in society, such as the free market. The classical liberal state is limited, which means it does have to perform or arrange for a number of important public tasks. Besides defense, police and judiciary this mainly concerns a minimal amount of welfare arrangements, some environmental regulation, or other issues that cannot be dealt with through the markets.
Libertarianism and social liberalism both originate from the nineteenth century and they constitute the two contrasting poles of the liberal spectrum. Libertarians think the classical liberals allow the state to grow too big. They favor a stricter protection of individual rights to life, liberty and property which to them ensures a just and good functioning society, where free people will be able to use their talents and cooperate in strictly voluntary ways. Some, like Murray Rothbard or Hans-Hermann Hoppe, argue this society can totally rely on spontaneous order for the provision of all necessary services and therefore want to abolish the state completely. Others, such as Ayn Rand, think there is a need to publicly organize defense, police and judiciary.
The social liberals (liberals in the contemporary American sense), such as John Stuart Mill or John Rawls think the libertarian and classical liberal ideas lead to social injustice. They argue that individual flourishing demands a fuller, positive kind of liberty (rights to), which enables individuals to fully develop themselves. Individuals should be able, especially through education, to learn skills and get knowledge to use their natural talents, at the labor market and elsewhere. Otherwise the idea of liberty is just formal, lacking any practical meaning. Concern for social justice also entails the redistribution of income (through taxation), to ensure a welfare system (social security, public health) that takes care of the less fortunate. This leads to a much bigger role for the state than in the other two liberalisms.
Interestingly, these differences also show up in the liberal views on international relations. Libertarians favor the least active (state) interference in world politics, classical liberals recognize the implications of uneven power distributions and believe in the spontaneous ordering effects of the balance of power, while the social liberals are supporters of international organizations and international law.
Needless to say this is just a very short description of the three liberal variants. Much more can also be said about the reasons to discard the other forms of liberalism that figure in the public debate. Still, in my view, this division into three stands up to critical scrutiny, is methodologically sound and therefore by far the best way to sort the liberal mess.