hurk
political terminology is just so obnoxious
"liberal" in the US does not mean the same as "liberal" in europe and it does not mean the same thing as "liberal" in history nor the same as "libertarian" or "progressive"
"conservative" also has changed meaning over time
"socialist," "authoritarian," and "anarchist" are the closest to being consistent but even socialism has drifted into moderate territory over time
Basically, this is the closest thing to a "standard" world set of terms:
Liberal: supports civil freedom and economic freedom (US libertarian) and supports progress in a classical sense; in this view,
Anarchists are extreme liberals
Conservative: supports economic freedom but restricts civil freedom (US conservative), and supports the status quo;
Reactionaries are extreme conservatives, supporting a return to previous times
Socialist: supports civil freedom but restricts economic freedom (US liberal) and supports progress in a keynesian sense;
Greens are very similar, but tend to be more moderate economically and place a greater emphasis on the environment;
Communists are extreme socialists
Authoritarian: restricts both civil and economic freedom (not common in the US) and supports a strong state;
Fascists are extreme authoritarians
Note that none of these say anything about what kind of government it is. You can have a liberal or a communist dictatorship (Napoleon and Stalin) and an authoritarian or reactionary democracy (Putin and Annoying Orange).
I consider myself a social democrat or green, in other words a moderate socialist that denies communism and many tenets of Marxism.