(Of course there is no such thing as a "social democracy", in the sense that the government structure is modified from a "non-social" democracy. But there can be democrats who push for a socially oriented governance. For example: Let's have affordable healthcare. Yes, that means that it cost more for rich people..
Democrats here means "people who want to take part in a democracy". not the US party. Not that they are liberal in the European sense either.) )
That's actually largely the case in Western/Middle Europe.
> marxist/communists in the far-left parties (and sometimes the whole party)
Which are often not seen as socialist. Social/socialist typically signals that the party is inside the system supporting political spectrum. "communist/marxist" usually signals that the party is at least partly outside the system supporting political spectrum.