I have previously answered a closely related question here, however, the question was removed due to being in breach of the rules, so I will put my answer to good use here and edit it to conform and better answer the question being asked in this case.

Edit: Since this was pasted from another answer, I forgot to specify what I was (in my head at least) comparing. What is below is more so a focus on National Socialism (or Nazism) and the USSR's adaption of Marxism.

​

Since we are speaking about ideologies and political theory, I shall first define ideology. Ideology is, although differing based on definition, essentially how humans assign structure to the world around them, and therefore go about understanding society, along with many other facets of reality. Thus, individuals with different understandings of society produce unique models of arriving at the "ideal", whether that be, in the case of the National Socialist (Nazism) state, lebensraum, or the Marxist state, communism.

Now, on to fascism and communism. Fascism was first implemented by Benito Mussolini and is a primarily twentieth-century phenomenon. Although extremely ambiguous and debated whether it even classifies as an ideology (for the sake of this answer, I will assume it to be so, focusing on Nazism as a sub-variation of fascism in its most extreme manifestation) fascism encompasses radical nationalism, or ultra-nationalism, along with authoritarianism, totalitarianism, and militarism. It harbours a deep undercurrent of anti-intellectual abstraction and favours power, action, emotion and instinct. Thus, the state and economy are heavily geared towards the military. However, fascism itself has few intellectual father figures and differs from example to example, such as Benito Mussolini's Italy and Adolf Hitler's Germany. Since Hitler produced his own work, Mein Kampf, and Nazism is distinct from other forms of fascism in its racial extremism etc., some argue that it is distinct from fascism altogether. It can be seen pragmatically (in an attempt to produce a viable answer) as a sub-variation of fascism, more extreme in its interpretation of the world, and therefore ever more radical in its ambitions and methods. It is for these reasons we can observe the genocide of millions of humans, essentially the destruction and eradication of minority populations in Europe, including, notoriously, the Jewish population, along with disabled individuals, Romani (gipsy), and the eastern Slavic population. The mark of Nazism, therefore, is a large stain on the twentieth century and the evil which manifested was a protrusion in every corner of the globe, felt by almost every individual, and remains a reminded of the depths of the human psyche and how it can exhibit itself at the expense of others.

Communism, however, is debated to have never truly manifested. If we adhere to Karl Marx's interpretation of history, and to his prediction that society will eventually arrive at communism, we can see that the pre-conditions for communism never truly occurred, and neither did communism itself. He interpreted history as a process of class struggle, with one class consistently exploiting another. He proclaimed that currently (capitalism) is the final stage of ancient exploitative class relations, and it will deteriorate, with the working class (proletariat) being produced as a byproduct of class exploitation, digging the graves of the exploiters (bourgeoisie). Marx viewed the state as a foreign entity oppressing society, manipulated by the bourgeoisie into consolidating and exhibiting their power over the proletariat. Communism, therefore, would be stateless and classless, among other characteristics. None of this was met in the twentieth century. What was arrived at rather, were socialist autocracies whereby the cult of the leader was employed and the entire state apparatus engineered to exalt the leader. It was in many of these states where the population suffered under poor conditions, work camps, poor economic policy, and famine. Most notably, Joseph Stalin's reign was plagued with what Aleksandr Solzhenitsyn has dubbed the gulag archipelago, literally, numerous work camps in which conditions and sentences were notably poor and human rights were not respected. As well as this, like in the other autocratic states of the twentieth century (such as Duvalier's Haiti, Mengistu's Ethiopia, and Ceausescu's Romania), the secret police, in this case, the NKVD, unleashed a period of terror, arresting countless innocents and torturing them into submission, later executing them as traitors to the state. The use of state terror alongside mass internment differed from the Third Reich's holocaust, as the official ideological predisposition of the Third Reich (National Socialism/Nazism) demanded the eradication of particular ethnic groups.

What you will notice here is how fascism manifested in various ways, each differing, making it an ambiguous and unclear ideology when compared to Marx's revolutionary communism. In this answer I have examined a sub-variation of fascism, Nazism, where racial superiority and inferiority was preposed and in Hitler's Mein Kampf, and adopted as the official state ideology under Hitler, thus leading to the engineered slaughter of millions through death camps, terrible conditions, execution, etc. Twentieth-century "communism", however, did result in the death of millions, but this was not one of the many values outlined by the various leaders. It was more-so a byproduct of authoritarianism and poor economic policy, alongside politically motivated eradication of certain sub-populations and political competitors, for example, the Soviet Kulaks under Joseph Stalin.

Sources Consulted:

Brown, G.W. 2018, The concise Oxford dictionary of politics and international relations: edited by Garrett Wallace Brown, Iain McLean, and Alistair McMillan, Fourth edn, Oxford University Press.

Hitler, A. & Murphy, J. 1942, Mein Kampf, Hurst and Blackett.

Marx, K. & McLellan, D. 2000, Karl Marx: selected writings, 2nd edn, Oxford University Press.

Rees, L. The Holocaust: A New History, Penguin.

Wetherly, P. 2017, Political Ideologies, Oxford University Press.