@lemonpepperlady
If it walks like a duck, quacks like a duck, etc....
No. Hitłer used to different definition of ʼsocialismʼ than the genersl nomencłature we would apply today.
In a 1932 interview, Hitler described his understanding and application of socialism:
Why’, I asked Hitler, ‘do you call yourself a National Socialist, since your party program is the very anthesis of that commonly accredited to Socialism?’
‘Socialism’, he retorted, putting down his cup of tea, ‘is the science of dealing with the common weal [health or well-being]. Communism is not Socialism. Marxism is not Socialism. The Marxians have stolen the term and confused its meaning. I shall take Socialism away from the Socialists.
‘Socialism is an ancient Aryan, Germanic institution. Our German ancestors held certain lands in common. They cultivated the idea of the common weal. Marxism has no right to disguise itself as socialism. Socialism, unlike Marxism, does not repudiate private property. Unlike Marxism, it involves no negation of personality and, unlike Marxism, it is patriotic.
‘We might have called ourselves the Liberal Party. We chose to call ourselves the National Socialists. We are not internationalists. Our Socialism is national. We demand the fulfilment of the just claims of the productive classes by the State on the basis of race solidarity. To us, State and race are one…
https://alphahistory.com/nazigermany/hitler-nazi-form-of-socialism-1932/
This system was rooted in race and patriotism, and did not refer to means of production or property as pillars.