In the rest of Europe, it does tend to break down in the way you describe. In 2009 (not sure if still the case), Denmark had a centre-right party called Venstre in government ("The Liberal Party"), and a much smaller party Radikal Venstre in opposition ("The Social Liberal Party"). This pattern (with or without the smaller one) tends to be the pattern in most of Europe I believe.

However, the article is discussing US Politics, so that is where the confusion arises.

I would like to argue that the {Liberal => Social liberal} mapping comes from JS Mill in the UK in the late 1800s, but I'm sure it originates before then.

Note also that the Lib Dems, a merger of the Liberal Party and the SDP, were not right wingers (Liberals) and left wingers (Social Democrat Party) merging, they were a historical Social Liberal party (Lib) merging with a relatively right wing spin off from Labour (SDP).

Here we tend to use 'neo-liberal' to describe the laissez-faire attitude towards economics.

I do find it peculiar, though, that "neo-liberalism" is of a different form than "liberalism", and hence not really "new liberalism":P

Way back when, (Whigs and Tories era), the "Liberals" we're the ones arguing for free markets as opposed to Feudalism. This is where attachment of the word "Liberal" to free market-ists originates, I think.