Neoliberal economic policies have nothing to do with liberal social policies. They are as linked as the German Nationalist Socialist Party was to socialist economic policies. Whenever these two words come up, someone invariably links the two as though they are spiritual cousins, and I don’t like that. It should be very clearly stated each time these words are conflated, or compared, that neoliberalism liberal, and that people who would describe themselves as liberal are entirely against neoliberal economic policies, which are largely carried out by corrupted politicians on both sides of the political aisle. Lest we mince words; neoliberals are at the opposite end of the political spectrum to liberals.
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.