Well yes, the "Right" and Neoliberals are the same thing. A lot of what is getting lost in translation is that a lot of people do not want a return to the status quo of liberalism because it has rather reliably created this cycle.

Neoliberalism was coined in the 70's and 80's to describe a change to classical liberalism a'la outlines of the defining features of "Liberalism" coined by philosophers like Locke and Hume. Neoliberalism is a push for deregulation of things that get in the way of business or interests and removal of safety net systems. Think Reagan and Thatcher.

"Colloquial liberalism" is more or less a bastardization of a sort of middle of the road progressivist vibe that sets itself as the opposite of "Conservative" ones. This is more like an advertising thing for individual parties. They use "liberal" and "conservative" to market themselves to their audiences. You are supposed to get the vague impression that conservative means things like fiscally sensible or traditionally valued while "liberal" is taken to mean focused on expanding personal rights or spendy.

The problem is that colloquial libralism and actual philosophic liberalism overlap in parties like the Democrats while Conservative parties like Republicans deny that they are philosophically speaking also Liberals. So when people on the left say they hate Liberals they are meaning both Democrats and Republicans because neither of those things strictly speaking are considered "left" except in relation to each other.