I've never, ever heard a social democrat party called liberal before, except when it's a foaming-at-the-mouth slur from someone who literally can't tell a Marxist from a Nazi.
(I usually find it means centrist (i.e. neoliberal) when people are self-describing.)
Not sure hyphenating "center" to "left" or "right" adds any meaningful granularity, but yes, I was criticizing that about the US a minute ago.
Yeah, it's crazy. And doesn't reflect actual political opinion in the US even a little bit.