You're close.
I would describe it as being the most limited government with the highest degree of subsidiarity on the one extreme with the most centralized and most interventionist statism on the other extreme.
In the former case, morality, economic activity, etc. are dictated and formed by voluntary associations like churches and business associations while in the latter all human activity is subject to state dictation.
I would not describe the former state as "anarchy" - most self-described anarchists are collectivists who believe in replacing the existing state with an even more powerful state consisting of rule by labor unions or similar organizations. To me, these "syndicates" are indistinguishable from soviets and therefore from Communism proper.
The former is consistent with both traditional American conservatism which was based on a limited government according to the US Constitution and with traditional European conservatism, which was based on the pre-absolutist, voluntary allegiance to a monarch who was restricted in his authority by tradition and by subsidiarity.
What I'd say is that Communism and Nazism are the left and right extreme versions of Statist and collectivist ideology.
Your description would be more convincing if you had given us a substitute axis for left/right distinctions to replace the liberty/statism axis you've rejected.
Because both Communism and Fascism/Nazism make the state the highest authority, give the state absolute power of the lives and deaths of its subjects and replace traditional systems of morality and interpersonal behavior with a state-implemented, state-promoting ideology, they are both on the far left of the left/right continuum.
I would recommend that you read Jose Donoso Cortes' essay (really a parliamentary speech) entitled "Catholicism, Liberalism and Socialism" in which he shows how state interventionism increases as people cease being inner-directed (i.e. doing the right thing because their well-formed Christian conscience inspires them to voluntarily behave in socially productive ways) and become other-directed (only the law and the accompanying punishment inspire them to behave in any certain way - they have no inner compass and are dependent on external force for moral action).
Don't mean to waste bandwidth with two posts in a row, but I believe I laid out the case for why we cannot merely have the left/right political axis you
For one, circumstances change and who is 'conservative' when viewing a particular time in history is difficult to discern (not in the sense of status quo but some abstract definition of the term.) Another is that people who subscribe to what I'd consider views antithetical to liberty may still find a home on the right. Certainly religious authoritarians hostile to leftist social and political movements may be rightist but not necessarily standard bearers for liberty.
I just think the axis, though it is helpful, is not sufficient. While Nazism and Communism are two sides of the same coin and can often resemble each other, too much in the Nazism that succeeded (as opposed to Strasser's vision) does not display the same leftist vision of communism or 'social democracy.'
I don't disagree with you as much as you think. I just think that for these categorizations to have meaning, one must also think of the social conditions of the time and where a particular movement finds its strongest base of support.
I'm not hostile to the idea of a liberty/statism axis, I just don't think it fits completely. It would mean that no totalitarian regime could ever be of the right. I just don't find that to be the case. I read far too many, even here at FR, that seem hostile to liberty on a great number of topics. I would not then consider those people 'leftists.'