Hitler was an Austrian but the Austrians are a Germanic people, be careful when you talk about Austria and this period as some wil try to tell you that they were the first victims of Hitler's expansionism, they weren't, the vast majority of Austrians supported the Anschluss, be very wary of modern Austrian and German victimology.
The Nazis overwhelmingly identified themselves with German culture, ergo to be a Nazi was to be German, there is a very unpalatable fact that modern Germans try hard to suppress, most of the atrocities committed during the war were committed by the Wehrmacht, not the S.S.
The S.S had specialised units and commands for killing people, the Wehrmacht just killed anyone.
For a quick reference look at the advance and retreat from Russia.