Maybe I didn't phrase it the right way... the point is that the occupied peoples in the West were generally viewed as more or less equal, as long as they weren't Jewish, homosexual, communist or part part other political, sexual or ethnic minorities.
In the East the Nazis treated everyone as a lesser human, some more than others, but still everyone. It's much easier there to not make the Nazi actions about minorities, but about everyone, and therefore it's easy there to simply associate Nazi = anti-Russian. In that sense the word survived and is used for todays Ukraine.