European Confusion over American "Liberals vs Conservatives"

I've been thinking more about the European (and specifically Friedrich Hayek's) confusion over the American use of the terms liberal and conservative.  To the European crowd, they think we have the terms backwards, since in Europe the term liberal tends to refer to the "liberation" of oneself from the control of the older monarchial governments that once prevailed across the continent.  An in fact, it was this "classical liberal" ideology that gave birth to the United States and dominated political thought here until the mid-20th century.

But that's when the "modern liberal" ideology, which has socialism in its genealogy, started taking root in this country and now dominates academia and mainstream media.  It is this new political thought that has commandeered the liberal identity and is not just a far cry from the European concept of a liberal, it is oftentimes a polar opposite.

And because classical liberal thinking makes up the foundation of traditional American culture and politics, those who hold the old ways close to their hearts are, by American definition, conservatives.  Whereas in Europe, the term conservative has always referred to those with a fondness for strong monarchies and the societal organization and law & order that come with that form of government.

So after 200 years, in a near complete reversal, the modern day liberal in the United States is now defined as someone with a preference for a strong government (but not a monarchy) and a strongly organized society, a sort of "moderate socialist".  Meanwhile the term conservative is now defining people who prefer smaller governments and more individual freedom.

Hayek writes about his confusion over our use of these terms in The Road to Serfdom and I've seen the same sentiments echoes repeatedly in German and British media.  It's pretty interesting though how we use these terms so differently and how we arrived at this point.