There is a lot of confusion -- no doubt. This has to do with the new usage of the term "liberal" to describe Democrats or people on the left, when historically, liberal meant people on the right, like Libertarians or Republicans. As a result, we now describe free-market liberalism as "classical liberalism", to distinguish it from modern "social liberalism".
To further complicate things, pundits on the left have attempted to associate the uglier side of left politics (namely, fascism) with the right, so you have a lot of people calling neo-nazis "far-right", when in reality, National Socialism was a leftist movement. Hitler was a "liberal", in terms of being a believer in large-scale government intervention in the markets.
Conversely, the USSR was and China is "conservative" in the classical sense. That is, they believe in government intervention in markets, which was called conservatism 100 years ago, and is called liberal today.