Yes, there are different ways authoritarianism can play out. Not all forms are equally problematic. Certainly does become a problem when it’s tyrannical, which is the case with totalitarianism. Both fascism and communism are totalitarian forms of government.
When people say that nazism (national socialists) is actually far-left rather than far-right politically, I’d say 1.) it doesn’t really matter since the end results wind up nearly indistinguishable, and 2.) when it comes to the political spectrum if you far enough you’ll loop back around to totalitarianism.
Call it what you will, but the results are still the same.
Democratic forms of government (quite literally) diametrically oppose totalitarian forms. So whether one starts out heading right or left, politically speaking, isn’t of real consequence here. Either way, they arrive together on the opposite end of the political spectrum.