@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
And I truly understand this part: "They destroyed all who were different from them." ...even within their party.