It's all a bit silly, really.
Classical liberalism is libertarianism - if you take the William Gladstone era as a reference. von Mises and Hayek built upon it and this spurred the (professed) politics of Thatcher and Reagan: strip away the state and let everything be free.
In parallel, socialism emerged and was adopted across Europe and China but was rejected in America for a variety of reasons - mostly the Cold War, where it was "un-American" to be a leftist, socialist or communist. Since McCarthy, it has been largely taboo to identify as any of these.
So the American left had to find another label: it chose Liberal to mean "not conservative". But here is the problem, classical liberalism is one of the main tribes of conservatism. Just listen to how the recent Tea Party and all its various adherents promoted "libertarianism" whilst at the same time disparaging "liberals". So, in America today, "liberal" can mean almost anything. Hence the massive confusion.
I highly recommend that people discard the label "liberal" as its meaning has been balkanised.
Instead, try to use these:
Reactionaries or Paleoconservatives - nationalist, protectionist, anti-abortion, pro-gun etc. Usually but not always "free markets within our borders", but can be quite statist. Often champion the past as a golden era, promoting "the narrative of decline". Donald Trump and Pat Buchanan.
Libertarians - free trade & open borders, reduce government size & influence; usually pro-gun and anti-abortion but not always. Ron Paul, Rand Paul, Thatcher, Reagan, Daniel Hannan, von Mises, Hayek.
Centerists - a mix of left and right, normally "globalist". Usually champion "the narrative of progress" so sometimes self-identify as "progressive". Clinton, Obama, Blair.
Socialists - redistributionist statists but can self-identify as "progressive" - Bernie Sanders, Jeremy Corbyn
Communists - the state is everything, you do what it says - Xi Jinping, Deng Xiaoping, Mao Zedong, Stalin, Lenin
Note: Marx was, paradoxically, a libertarian. He believed that in the final revolution, all need for government would be swept away and the people would just spontaneously be benevolent. He simply viewed communism as a necessary step on that journey. The problem is that this path to the final revolution tends to get stuck at the communist stage - and the all-powerful central committee won't give up power.
Note 2: "progressive" is as catch-all as "liberal", but can be define a bit more unambiguously. It generally hinges around the idea of promoting social reform, because not only can a better world can be achieved but it should be actively be pursued. This is the narrative of progress and almost all political movements, apart from Reactionaries and Paleoconservatives preach it; so it can included libertarians and communists, who don't agree on much. So "progressive" is best avoided.
My naive idea is that if this terminology becomes widely used, political debates might make a lot more sense!