AskHistorians

There was a period in the early 30s when the communist and left-wing elements had been purged from the Weimar Republic, and the right-wing working-class German Workers’ Party hoped to court their supporters by renaming itself the National Socialist party. (Imagine if, in pre-Trump USA, the Sanders/AOC DSA had been expelled from the Democratic party, and the Tea Party tried to pull support from them by calling itself the Tea Party Socialists.) But they never adopted socialist ideology—the only thing they had in common was their working-class demographics. Socialism, communism, and anarchism all had their origins in the 19th-century Internationalist movement, which was expressly anti-nationalist—so the very name “National Socialism” was a transparent contradiction in terms.

(That said, Mussolini in Italy did have an early phase where he was a bona fide socialist, but the Italian socialists expelled him for his racism.)