Right-Wing Totalitarian - The most extreme and tyrannical of the rightist governments. As one can tell from the name, a brutal dictatorship that insists on controlling every element of their citizens' lives and watching them through a secret police that isn't afraid to get its hands dirty, while fanatically pursuing an extreme-rightist religious or racial ideology to boot. May or may not be actively committing genocide. RL examples: Nazi Germany, Mussolini's Italy, late Imperial Japan. RB example: The Columbian Commonwealth, you must've seen
that coming.
Reactionary Authoritarian - An authoritarian government that, while not as harsh as the RWT, nevertheless follows policies that pretty much everyone else would call backward and obsolete, if not outright Dark Age - and is more than happy to enforce these policies through force. Likely heavily influenced by traditional religion and to a lesser extent, deep-seated racism. RL examples: Tsarist Russia, Franco's Spain, the post-'Redemption' South. RB example: Bourbon France until its overthrow in 1871 (remember, there was no French Revolution, so the Ancien Regime was still leading France at that time).
Conservative Authoritarian - Your run-of-the-mill conservative dictatorship, not as gratuitously sadistic as the RWT and not as violently reactionary as the Reactionary Authoritarians, whether out of genuine quasi-benevolence on the leaders' part, pragmatism or just corruption and bureaucracy preventing them from being completely evil. RL examples: Chiang's Republic of China, Poland after the '26 May Coup, Greece under Metaxas. RB example: Tsarist Russia following the reforms of the longer-lived Alexander II.
Conservative Democrat - A conservative democratic government with a much stronger emphasis on social instead of fiscal conservatism. May follow laissez-faire or Keynesian fiscal policies. RL examples: The Republicans' social-conservative/evangelical wing (think Palin & Huckabee), the Tory Cornerstone Group, the Northern Irish Democratic Unionist Party. RB example: Tories following in the style of George Griffiths (Dan).
Market Liberal - A conservative democratic government with a much stronger emphasis on fiscal instead of social conservatism, or alternatively a classical liberal government that may follow a few socially conservative policies. RL examples: The fiscal wing of the Republican Party (think Paul or maybe Romney), Thatcherites in the Conservative Party, libertarians. RB example: Tories following in the style of Liam O'Falvey (Gunny).
Centrist - Exactly what it says on the tin. A moderate government that sits on the crossroads of pretty much every issue, taking in both conservative and liberal elements. May be genuine ideological centrists who feel that the 'middle way' is the best way forward, or flexible pragmatists not bound by petty ideology. RL examples: The PRI in Mexico post-1950, Irish Fianna Fail/Fine Gael, Blue Dog Democrats. RB example: Ciel Amherst-Shimazu's Centrists (Rosen), as one can tell from the name.
Social Liberal - A liberal democratic government with a much stronger emphasis on social rather than fiscal (classical) liberalism, supporting at least basic welfare and Keynesian economics in addition to socially liberal policies. RL examples: Most mainstream European liberal parties (especially by American political standards), Democrats in the mold of Nancy Pelosi, Canadian Liberals post-Trudeau. RB example: ...wow, this is hard lol. Celsius's new Egyptian nationalist party, the PDLF? Not sure if MMM's old party would fall here or under ML, either.
Social Democrat - A socialist democratic government with an equally heavy emphasis on both social liberalism and a welfare system. RL examples: The Scandinavian countries but Sweden in particular, Canadian New Democrats, most mainstream overtly leftist European parties. RB example: The SPD in the HRE, which is basically the same as the real SPD, just bigger.
Radical Socialist - Your run-of-the-mill socialist dictatorship, not as gratuitously sadistic as the LWT and not as violently ideological as the Socialist Authoritarians, whether out of genuine quasi-benevolence on the leaders' part, pragmatism or corruption and bureaucracy preventing them from becoming completely evil. RL examples: The USSR between 1921 and 1928, Mexico just after the Mexican Revolution, Castro's M-26-7 before he came to power. RB example: The Levellers.
Socialist Authoritarian - An authoritarian government that, while not as harsh as the LWT, nevertheless blindly follows its extremist ideology without once thinking practically, and damn the consequences. In RB they're more likely to be influenced by
Sorelian syndicalism given that Sorel was Director of the French Commune, basically making him our Lenin analogue. RL example: The USSR between 1918 and 1921 and again under Brezhnev, Mexico under Plutarco Calles, Mao's Great Leap Forward. RB example: The Commune of France - most of the time, anyway.
Left-Wing Totalitarian - The most extreme and tyrannical of the leftist governments. As one can tell from the name, a brutal dictatorship that insists on controlling every element of their citizens' lives and watching them through a secret police that isn't afraid to get its hands dirty, while fanatically pursuing an extreme-leftist ideology to boot. May or may not be actively committing genocide. RL examples: Stalin's USSR, Pol Pot's Cambodia, Mao's Cultural Revolution. RB example: The French Commune at their worst.