Using socialist was a marketing decision to win over the populace who were in dire straits financially.
The nazis were no more socialist than North Korea is a democratic republic.
There was certainly “socialists” in the Nazi movement, namely Goebbels and Ernst Rhoem, who advocated a complete government takeover of German industry. This was one of the reasons he was eliminated, because he scared off the German industrialists, who Hitler needed to build the war machine.
What’s interesting is to contemplate what would have become of the industrialists, once they were no longer needed.
My Great Grandfather fought in the Civil War on the other side, which slightly taints my view of that conflict. Dream on.