Neoliberalism isn’t libertarianism though. It very specifically refers to an economic model. Effectively it’s a shifty way of referring to modern forms of laissez faire capitalism. So as not to bring up disturbing connotations of child labor and Pinkerton’s smashing union heads. If there’s a major difference there it’s that the neoliberal position is that there should be government involvement in the market. But only in so far as it exclusively benefits big business and the finance sector. Who will then magically shower wealth on those boot strap pulling poors. Because reasons?
While modern right wing libertarianism has completely embraced (and seems mostly concerned with) the neoliberal economic model. The two aren’t synonymous. Libertarianism covers a lot more topics than just economics, and neoliberalism is really only concerned with non-ecconomic topics in so far as they might effect the bottom line.