Credit
sphagnum
Liberalism = belief in limited government (that is to say, government limited by constitutional powers, not "small government") and individual liberties. Classically, the Republican and Democratic parties have both been liberal parties. The term "liberal" veered off to mean "expansion of rights and government services" in the US, with conservatism developing to mean the opposite, but ignore that because it's an aberration from the worldwide meaning.
Socialism = worker control of the means of production. Out of fear of socialist revolution, capitalist (liberal) nations made compromises leading to the development of social democracy.
Social democracy = liberal state with an expansive welfare system. Social democracy came out of reformist socialists who gave up on the transition to worker control combining with reformist capitalists who feared revolution. This is what prevailed in western Europe and the Democratic Party for most of the 20th century.
Neoliberal = a reaction to social democracy, a return to belief in small government, cutting taxes and services, and turning to the market for solutions. This was pioneered by Pinochet, Thatcher, and Reagan but became basically liberal orthodoxy by the 90s. It doesn't matter whether one is socially progressive or not, it's about economics. Hence why Bill Clinton was also a neoliberal ("The era of big government is over!", his welfare "reform", etc.) and why socialists often argue that Obama was not really a social democrat but a neoliberal, at least to some extent (his desire for a grand bargain that would cut entitlements, Obamacare turning out to be Romneycare, etc.)
We are now entering a period where neoliberalism is clearly failing/has clearly failed, and some combination of pro-socdem/pro-demsoc support is on the rise. Demsoc/democratic socialism = socdem but further beyond/reformist socialism/using socdem as a stepping stone to get to the end goal.
