@Kent C:
Yes, that sounds a little confusing, unless you were extensively educated in German history (which I was).
The "National Socialists" were the Nazis. "NATIonalsozialisten". When you pronounce the word in German, it starts with the sound "NAZI". Thus, the "Nazi"s. The Socialists were a completely different political party. And one whom the Nazis exterminated during their rule. Same as the Communists. They destroyed all who were different from them. As is common in dictatorships.
I have some education in German history but not to your extent. The book mentioned earlier "Liberal Fascism" gets into a detailed differentiation within Germany and also Italy's fascism (which was not 'anti-Semitic').
And I do understand there are differences in 'parties' even though the 'type' of governing policies can be quite similar - where the state is sovereign, but where the enforcement is different. So in Europe mostly, you'll have a Socialist Democrat party, a Democrat Socialist party, a Social Democrat party, a Labour Party, etc. etc. All basically socialistic in nature, sometimes in bed with each other and sometimes at each others' throats Similar to the Socialist party and the Liberals here and the Republicans and Libertarians as well.
And I truly understand this part: "They destroyed all who were different from them." ...even within their party.