I'm pretty sure we're just the confused ones here. left, liberal, democrat, republican, right, libertarian, socialist, conservative.
Those words are giant tents. I have a book that argues that Hitler was a "liberal" and another that says free-market military-backed imperialism is "liberal democracy". I have another that argues the state-communism of China and the USSR are "conservative".
So I have no idea what people mean when they use those words.
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.
They mean nothing in practice because of bizarre narratives like that.
Before taking power, the Nazis caucused with the National Conservatives, the Free Conservative Party, and the German Conservative Party.
German leftists were first to the concentration camps under the Enabling Act of 1933. Under the Röhm Putsch, the Nazis killed and outlawed the left-leaning faction of their party. Under the Commissar Order, Hitler prioritized the death of leftists in conquered land. Socialists, leftists, liberals and communists got their own special badges at the death camps (https://en.wikipedia.org/wiki/Nazi_concentration_camp_badge#...)
The USSR and China are autocratic state-run corporatists. They are conservative in that they are effectively industrialized reactionary feudalism with integrated propaganda to prevent populist revolution.
And finally, some may enjoy calling an intentionally plutocratic state liberal, but it's essentially autocracy without coronation ceremonies.
The confusion here isn't that the ideas themselves are confusing. The historical record is abundantly unambiguous. However some don't like it so they do revisionism and taxonomy hand-waving to try to confuse people. But that's the nature of power.
That's because they were reactionary monarchists. The nationalising was a throwback to 18th century imperialism. That's a rather extreme form of "conservative". Its not like we're talking worker self directed cooperatives regulated by government for the public good.
Marxist in first international was about extending democratic principles to the organization of labor. When you have a single party dictator snatching up enterprise, you don't have first international.
Besides, the terms are for camps more than anything. It's an affinity, not a taxonomy.