"Fascism" generally was the preferred term in Soviet propaganda and historiography over "Nazism" for a variety of reasons, but probably the main one is that fascism is, from the Soviet point of view, the more broadly encompassing term.

The way that Marxist thinkers defined fascism and explained its rise in the Interwar period was that as bourgeois states reached crises from the inherent contradictions in their socio-economic organizations, the ruling classes of these societies used "fascism" basically as a way to maintain their power by distracting the working classes from organizing on a class basis (a la Marxism). Antonio Gramsci, if I'm not mistaken, is one of the big Interwar communist thinkers who popularized this view (even though he was Italian, not a Soviet). So from this point of view, Nazis and Nazism were just one flavor, if a particularly virulent and power one, of a variety of fascism that was, from the Soviet view, controlling most of the bourgeois world and threatening communism.

There is some element of truth to this definition, as both the Italian Fascists and the German Nazis consolidated their holds on power by coming to agreements with national conservative establishments, their respective militaries, and the larger industrialists. Similarly, a lot of conservative dictatorships in other European countries either openly collaborated with local fascist parties (Franco's Spain), adopted a lot of fascist-inspired imagery and organization (the Metaxas regime in Greece), or tried to create their own fascist movements from scratch (Austria's Austrofascism).

Of course, the Soviets tended to use "fascism" even more broadly to include any leftist or Marxist groups that Stalin disliked - Germany's Social Democrats were called "social fascists" and Trotsky was regularly denounced as a fascist. The idea here was that these groups were secretly in league with the antirevolutionary bourgeois classes fighting to disrupt the true standard bearers of the working class revolution (ie, Stalin).

Finally, circling back to the Eastern Front of the Second World War: even though the Germans were the lion's share of the forces fighting on the Eastern Front, using "fascists" is a helpful catch-all term that can encompass not only the Germans, but also the Italian, Romanian, Hungarian, Slovakian, International SS, and even Spanish units that were all fighting in the USSR.

Talking about fascism allowed the Soviets to focus on the international and class-based aspects of the conflict and ignore specifically Nazi-related aspects such as the Holocaust, that didn't fit in particularly well with a Marxist-Leninist interpretation of history.

In addition to being a catch-all term for Germany and its Axis allies as /u/Kochevnik81 outlines, Nazi was also a problematic term for Soviet rhetoric. The word is a corruption of National Socialist and the firm opinion of the USSR's propagandists was that there was nothing socialist about the Third Reich. From their perspective, associating Hitler's state with socialism was an insult to socialism in general and one that needed to be avoided.