As an American whenever we discuss WWII we always hear the "Nazis did this..." and "the Nazis did that..." but not "the Germans did...". We name Japan, USA and Russia as just countries, not by the ruling political party. But why don't we do it for Germany? I've heard that the Nazis didn't have the full support of the people, but it seems that would have been the same for other nations too. We don't hold the Democratic Party responsible for the bombing of Nagasaki or Hiroshima, or the internment camps. Both are recognized as American acts, but routinely we hear about Nazi action during WWII instead referring to it as German action. The holocaust is one such event that is blamed on the Nazis but not the German people that made up the bulk of the Nazi hierarchy and was carried out with support from the German people(maybe not the mass executions, but the night of broken glass and other general support).
For one thing the Nazis didn't call themselves Nazis. The term Nazi was actually an insult directed at the NSDAP (Nationalsozialistische Deutsche Arbeiterpartei). It means a foolish person. It wasn't the name that the members of the NSDAP chose for themselves. It was used by their political opponents.
The reason it was chosen to be used to insult the NSDAP is because the Nati in National sounds like Nazi. Germans who left (as in left because they didn't support the NSDAP or fled because of persecution) Germany took the term Nazi with them and popularised it in the rest of the world.
http://www.etymonline.com/index.php?allowed_in_frame=0&search=nazi&searchmode=none
I am not sure your observation is even true, as I see German and Nazi used interchangably in most discussions.
I also see the term "Soviets" used much more then "Russians", but then again it could be reffering to the state not the political party.
Anyway, even if it is true, I don't think it is a post-war construction. I saw plenty of news headlines of that era ths at used extensivly both terms "Nazi" and "Germany" (and also "Reich") I can only speculate about the reasons. So the questions should be why did people at that time already use that kind of distinction?