Fascist Germany and Stalinist Soviet Union had many things in common: an authoritarian government with a cult of personality regarding the leader, suppression of civil liberties, brutal police forces, no political party pluralism, extreme nationalism, fear of criticizing the authorities, etc. So how do you distinguish authoritarian communism from authoritarian fascism?
Fascism and Communism are fundamentally different socio-political systems. You use Nazi Germany and the Soviet Union as your examples, so let's examine those two nations and see the differences. I'll have to answer in two parts, due to the length of the necessary information. The first part will discuss their economic systems, while the second part will discuss the political structures.
Part 1: Economic Systems
The USSR and Nazi Germany had completely different economic systems. The Nazis favored privatization (the word was literally coined to describe their policies) and market forces, as opposed to the planned economy of the Soviet Union. According to a study published in The Journal of Economic History (published by the Cambridge University Press):
Irrespective of a quite bad overall performance, an important characteristic of the economy of the Third Reich, and a big difference from a centrally planned one, was the role private ownership of firms was playing - in practice as well as in theory. The ideal Nazi economy would liberate the creativeness of a multitude of private entrepreneurs in a predominantly competitive framework gently directed by the state to achieve the highest welfare of the Germanic people.
The Nazis pushed for intense privatization whenever they got the chance:
Available sources make perfectly clear that the Nazi regime did not want at all a German economy with public ownership of many or all enterprises. Therefore it generally had no intention whatsoever of nationalizing private firms or creating state firms. On the contrary the reprivatization of enterprises was furthered wherever possible.
It should also be noted that these policies failed tremendously, causing an unparalleled mortality crisis in Germany. According to a study published in the journal Economics and Human Biology:
The results imply that Germany experienced a substantial increase in mortality rates in most age groups in the mid-1930s, even relative to those of 1932, the worst year of the Great Depression. Moreover, children’s heights - an indicator of the quality of nutrition and health - were generally stagnating between 1933 and 1938, but had increased significantly during the 1920s. Persecution, by itself, does not explain such an adverse development in biological welfare; the non-persecuted segments of the German population were affected as well.
All of this contrasts with the USSR's planned economic system. For all of its faults, it must be noted that the Soviet system was successful in bringing about rapid growth. According to a study in the journal Comparative Economic Studies:
The Soviet Union grew rapidly by comparison with other countries at a similar stage of development... It is unlikely that the Tsarist economy would have done so well had the 1917 revolution not occurred. [...] Soviet GDP increased rapidly with the start of the first Five Year Plan in 1928... While investment certainly increased rapidly, recent research shows that the standard of living also increased briskly.
In other words, while Nazi Germany had an economy based on private ownership, market forces, and military development, the USSR had a planned economy, based on state ownership of the means of production, which focused on general industrialization and modernization.
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