How exactly would you define 'correct' in this context?

Not by any stretch. A literal Nazi would be a member of the NSDAP a political party. All served under NSDAP government and, though party membership was very much encouraged, it was not a legal requirement. For example about 30% of higher ranking officers in the Wehrmacht were members, not a particularly large number and previous thread with a similar theme suggests 10% for the general soldiery. Not that this would exclude them from any culpability, the Wehrmacht committed atrocities as well (the myth that they where honorable where the SS wasn't is a common error) not to the scale of the SS however they were not labelled a criminal organization like the SS in the Nuremberg trials. The Waffen SS was the military wing of the Nazi party and therefore 100% of them were Nazis.

So factually "nazi" is not an appropriate demonym , however the common popular understanding simplifies it to anyone fighting for Germany in WWII was a nazi.