Did the term become bastardized by US? I wouldn't be surprised. Being a conservative doesn't mean what it used to mean either, and it has been taken over by "neo-conservatives".
Since the early 20th century in the U.S. it's meant something like "social liberal", market-oriented but in favor of a welfare state, more like what the SDU is today. And the opposite of "conservative" on issues like same-sex marriage, abortion, etc. Vaguely the same meaning of "liberal" that applies to the UK's Liberal Democrats. Actually not that far off, in terms of policies, from the meaning of liberal used by the German Freiburg-school ordoliberals, and their idea of the "social market economy".