Not exactly. National Socialists (Nazis) sometimes absorbed the nations they conquered (e.g., Austria, Czechoslovakia, and Poland) directly into the Reich so they were ruled by Germans. However, there were some satellites (e.g., Hungary, Romania, Bulgaria, Croatia, Vichy France) that were ruled by locals subserviant to their German overlords.
Communists (Marxists) may have have been "internationalists" at first but then developed the super nation-state of the Soviet Union by absorbing quite a number of smaller nations into Russia. The Eastern European satellite communist nations were governed by local communists who maintained their national identity, but were succeptable to Soviet military invasion when local communist hegemony was threatened (e.g., Hungary in 1956, Czechoslovakia in the "Prague Spring", 1968).
Again, I'm not talking about Communists (of which you might as well include the Spanish Communist Party of 1933) but the communist international which sponsored and supported the Russian Revolution, but recoiled when it went bad. The latter, the international, was a cadre of intellectuals, principally German and Polish, that grew out of the Bund der Gerechten, then the Spartakusbund, and then the Frankfurt School, which relocated to the United States in the 1930s. Both Cultural Marxism and Critical Theory as promulgated in this country owe their origins to that political heritage.
Note that this confusion (and possibly a deliberate one) existed well before World War II. Here is a little quote written in 1938 from Homage to Catalonia, by George Orwell:
In reality, it was the Communists above all others who prevented revolution in Spain. Later, when the Right Wing forces were in full control, the Communists showed themselves willing to go a great deal further than the Liberals in hunting down revolutionary leaders.Orwell understood and acknowledged that difference between the anarchists (communists) he had joined and the Spanish Communist Party, a Stalinist group. He draws the distinction because the former are the originators of the ideology that binds popular support to the dictators that have arisen therefrom. They are the source of "the beautiful lie" that gains Marxism its popular support, not just among the foot-soldiers of the movement, but among the theorists and apparatchiks seeking a piece of the action.[Snip]
Between the Communists and those who claim to stand to the Left of them there is a real difference. The Communists hold that Fascism can be beaten by alliance with sections of the capitalist class (the Popular Front); their opponents hold that this maneuver simply gives Fascism new breeding-grounds. The question has got to be settled; to make the wrong decision may be to land ourselves in for centuries of semi-slavery.
Do not underestimate the importance of the distinction. For it is the ideology of a society without landed gentry that is so attractive to the dispossessed. Hence, the difference between fascism ("you can (supposedly) keep your land" and communism ("socialize and redistribute all land from the get-go") is an important one, not only for the demographics to which they respectively appeal, but in how they express their respective dysfunctions. They are not both necessarily and inherently tyrannical, as we have seen reversal from fascism without catastrophic consequences. Here.
In many ways, the USA of the 1930s had become as fascist as the nations we were fighting. Certainly Roosevelt's control of the economy to supply the war was very nearly of that character. Yet the distinction I maintain between fascism and communism, that people still lived on the land of their fathers, is a powerful one, and a factor that played an important role in bringing us back from the brink of fascism as the War faded into memory, a memory hole we are at serious risk of revisiting today. Yet at no time was American fascism even close to its NAZI, much less Soviet parallels. It is the graduation of those difference upon which I argue their existence.
One can certainly draw parallels, but simply because America's WWII economy bore many resemblances to the NAZI system, does not mean that the latter was functionally equivalent to the Soviet State. And yes, I have seen the NAZI medallions depicting Karl Marx. I have read the quotes of parallelism from pre-War German sources, and I attribute much of that ideological affinity to political expediency, which is why it so easily evaporated the moment Hitler thought it useful to his ambitions.