No, you’re confused, bro. ‘Liberal’ is both a political identifier people use for themselves and others, and a series of policies and political ideals. Neoliberalism is a series of economic policies practiced by conservatives, regardless of the (D) or ® next to their names. If we were going to describe someone as a neoliberal, which people generally do not, the person being described would be almost the exact opposite of someone who would be described as liberal. The thing you said about being fiscally one way and socially another isn’t the definition of neoliberalism, that’s just an old line people say when they’re ashamed of being conservative and don’t want to come off dumb.
You can always count on a demented righty, often an off-duty cop, to show up dressed as a lefty to light a fire, break a window, or shoot someone. That’s why they’re always using that exact accusation against leftists, because they’re actually doing it.