That is correct. And the linguistic distinction was actually invented by the Soviets (and unfortunately adopted by the West), to enable them to divide the Germans into good ones (in the East, where actually more war criminals resided unpunished) and the bad ones in the Western zones.) But the concentration camps belonged to the German state not to the Nazi party, and the war crimes were committed by Germans not by specifically by the German ruling party members.
Note that the Nazis employed Ukrainians as guards at Auschwitz, and not Poles. The Nazis knew if they gave Poles guns, the Poles would use them to shoot the Nazi bastards.