Genocide is a characteristic of one major fascist regime. It is not a characteristic of all of them.
The regimes don't set out to conduct the genocide, that's not their initial purpose. It's a tool that they use. For fascists and Nazis the genocide and politicide is a consequence of their strong in-group/out-group philosophy. The Nazis didn't take over Germany to kill the Jews, they ostracized, murdered, and eventually committed genocide against the Jews in their efforts to take over Germany (and other territories as they expanded).
Communists used genocide less as a tool to direct their people's anger and more as a political tool to control a territory. Ukraine as an example. They didn't convince the Russian people that Ukrainians were an enemy that needed to be wiped out. They (USSR) permitted the famine to be so destructive so as to reduce the Ukrainian efforts for independence, and to make room for Russians to be moved in (or they took advantage of the opportunity to do this last part), further reducing the Ukrainian identity.
Lenin stated before the Bolshevik Revolution his goal to kill members of the bourgeoisie; he and his followers (such as Stalin and Mao) caused the deliberate death of more than 100 million people under their Communist dictatorships.
Pol Pot joined the French Communist Party in Paris during the 1940s, where he adopted genocidal Marxism-Leninism, as presented in the writings of Joseph Stalin and Mao Zedong. I'll let you look up the results of his work.
Maybe that wasn't how it went in the Holodomor, but it's definitely how it went in Dekulakization.