It's interesting distinction you are making here, but I'm not sure I understand it.
Would you not call the Red Army "communists" either, after all probably many of the soliders in the Red Army were just Russian (or Belarussians, etc.) who were conscripted.
In typical usage we say that "the Nazis attacked Poland in 1939", etc. In a totalitarian regime was there really any difference between being a Nazi and being a non-Nazi member of the German military? How about volunteers vs. conscripts? Would it be fair to call volunteers "Nazis"?
Looking at German insignia of WW2, almost every military award (like the Iron Cross) incorporates the swastika.
It seems to me that you are making a distinction without a difference, and that anyone fighting as part of the German armed forces in the period of WW2 can quite properly be called a Nazi.
To answer you, I’ll have to defer to what my father (WWII Airborne, combat vet, twice wounded) said many year ago.
“We hated the SS. Die hard Nazis. Never took them prisoner unless ordered to. The regular Wermacht guys didn’t bother us... but the SS, nope. Done.”
Clearly he - a man who was there and had seen them up close and fought them - made a distinction. So that was always my understanding as well. There were “Nazis”, and then there were “German Soldiers” to him. He also was part of a unit tracking down die-hards after the surrender. So again, I’ll defer to his distinction.
“Nazi” is the acronym for “National Socialist German Worker’s Party” - a political organization. Not all German soldiers, Luftwaffe, or Kreigsmarine personnel were Nazi party members. The SS on the other hand, for the most part, were.
As far as the Red Army - Not all Red Army soldiers were die-hard commies, either; if they were, then Stalin wouldn’t have needed to have NKVD commissars placed throughout the ranks, nor entire units of NKVD diehards to “police” the rank and file, rat out “defeatists”, and otherwise make life miserable for folks.
In other words - you have your fanatics (the minority), and then you have ordinary folk (the majority) caught up and forced into a situation they’d probably rather NOT be in, but are there nonetheless.