The whole point WAY back was that Fascist Italy's economic intervention, for example, was radically different than that of the Soviet Union's but was still quite extensive. Corporatism is drastically different than Command Economics. To make an awkward analogy, that hits home, Corporatist economics are incestuous rather than outright controlling like Command Economics. Both are centralized, but both use radically different mechanisms.
So, as I'll show further down below, they aren't even similar frequently in action, much less in ideology. I argue this because it matters to how the CSA is viewed.
Why do you say Police State? There are a lot of implications of those words, and Fascism didn't control its populace that way. That would be somewhat accurate for the Soviet Union, while Maoist China carried out much of its brutality through paramilitary social movements, which is rather different than a secret police.
And look? The actions, i.e. the what, are different, not just the justification.
The difference isn't all that much. In all three cases you are jailed, beaten or killed for actions that wouldn't be considered illegal in a free society. What exact organization carries it out and whether it is called liquidating class enemies, re-education or establishing order makes little difference to the people it is effecting.