In the Soviet Union Trotsky was the proponent of the first, while Stalin was a National Communist. Nazism is typical leftist/statist policies combined with some right-wing ideological elements, foremostly Nationalism.
Nazism also encorporated textbook fascism, which required industry to produce what the state required for its political agenda, yet still allowed them to profit handsomely from their efforts. I.G. Farben comes to mind.