You should learn what the word liberal actually means. Liberalism is a center-center right ideology and has both historically and now been at odds with progressive politics, up to and including aligning with fascists over leftists. It's been marketed as "everyone left of center" these days, but that's just not what the word means as a term. Think of the word "neoliberal ", and remember that neoliberalism is explicitly a return of the laissez-faire ideas of classical liberalism. Regardless, I said "aka democrats" specifically so people who aren't neck-deep in leftwing politics know what I'm talking about.

Moderate Dems (there are not moderate Republicans) are not liberals and don't call themselves liberals.

I mean they don't call themselves liberals, but according to what the term actually means in political science they're liberals (well, sort of, some are conservatives).