I think it does matter that it was socialism because socialism is the intermediary step to communism. If you read Mein Kampf where Hitler explains why he chose the colour red for his party it just rings hollow. He says it was a sort of fuck you to the communists who also chose red but in reality I think he was a secret Marxist. National Socialism was definitely statist and everybody had to swear loyalty to the fuerher and stuff. It's still slavish and lacks freedom. They had gesture politics with hand hand signal, just like the radical leftists with their revolutionary fist. It was still a cult, it was just framed in such a way as an opposition to an apparently more sinister cult. I view this very much as the Hegelian (or Kantian) dialectic in action.

They also had their euthanasia programs don't forget, where they would kill people with disabilities and such. They still treated their people like cattle and believed themselves to have authority over who gets to live and who dies. Lieben enwertes lieben and suchlike.

Whilst I acknowledge the actual communists were far more evil, I would still acknowledge that the lesser of two evils is nonetheless evil.