I think you're right. What most posters to this thread have failed to distinguish is that Communist USSR, Fascist Italy and Nazi Germany were all totalitarian. Top-down iron-fisted control was what they shared in common, not economic views.
Natural Law, as recognized in the U.S. Constitution, was abolished in favor of central planning and secular human control. That still holds true today in the EU, other socialist and Communist nations around the world, and with the American Left.
The totalitarian threat as described by George Orwell is still very much with us although the EU welfare states have substituted a committee of unelected bureaucrats in Brussels instead of one-man dictatorship. The U.S. is inching more and more in the same direction but with international corporations vying with bureaucrats for the "ruler" role.
The "man-as-God" idea of eugenics and elimination of "undesirables" fostered by such as American Margaret Sanger (Planned Parenthood's founder) inspired Hitler's appeal to pagan Germanic Aryan roots and "racial purity." Hatred of Jews was deeply embodied in the German (not to mention Western European) character. Combined with the economic misery brought on Germany by World War I, it rallied the masses behind Hitler in his drive for absolute power.
Whether Nazism was "socialist" or not begs the issue. The real danger to the world, then and now, is totalitarianism. It wears many costumes and tells politically palatable lies, promising Utopia for the downtrodden while passing favors to powerful elites. Does that remind anyone of any current American politicians?
Good post.