> The difference between a libertarian and a neoliberal is that a libertarian believes that markets and property rights (aka capitalism) are the end goal, and a neoliberal believes that those are powerful tools to achieve the goals of the social left.

This seems basically false. Neoliberalism is an economic philosophy (with, admittedly, social implications), and it's radically different from the economic views of libertarianism. Both are market-friendly and laissez-faire in a way that (serious) socialism and communism are not, but that's about the end of the alignment.

Neoliberalism is not appreciably a free market policy (with the caveat that two neoliberals, like any two economists, can disagree on anything). It's open to large amounts of government involvement, pushing monetarism and deregulation but not nonintervention. Nor is it strictly opposed to government taxation and spending; its objection to the Greek model is primarily one of direct government expenditure as opposed to spending via private sector contracts.

At least as actually practiced, neoliberalism is happy to use market interventionism in certain domains. Strict intellectual property laws, formally granted 'natural monopolies', and mass incarceration (for reasons other than violation of the non-aggression principle) are antithetical to libertarians, but they are the everyday fare to neoliberal politicians.

I think these are crucial differences, because they're the bulk of why 'neoliberal' is used as an insult. A look at the TPP fight clarifies the difference: libertarianism is all for free-trade agreements in principle, but opposed to the neoliberal contents of the actual document.