Neo-liberalism vs. conservatism and free markets...huh? (A little help?)

I'd post this in GD, but it would probably get lost. I'm doing some "annotated bibliography" entries for my graduate class, and I'm reading quite an interesting article about the effects of politics on educational reform and philosophies. As one might expect, the vast majority of the article points to all of the stupid things the right has done in order to "reform" education, which have only harmed it. However, the author seems to connect the concept of free markets exclusively to neoliberalism. Now, I see on Wikipedia's free market entry than the free market concept throughout Europe is connected to the term "liberalism," yet in the US, it's the domain of conservatives. Can somebody clarify what the hell is going on here?

At the time modern political labels emerged during the enlightenment, it was the liberals who opposed heavy-handed absolutist monarchies, the power of the church etc. In this sense, restrictions on trade were seen as a tool of oppresive government. Thus, liberalism as it was originally concieved was in favor of low or no tariffs.

In the US today, what is "conservative" and what is "liberal" may or may not have anything to do with the original definitions as established centuries ago, as our two political parties stake out positions on the issues of the day. Thus the confusion.