Although they differ in other important aspects, communism and (extreme) fascism are both forms of socialism.
Communism seeks to establish government ownership over the means of production through a revolution of the working class.
Fascism too seeks to establish absolute government control over the means of production, though the institution of private property is symbolically retained. In practice, however, extreme fascism is socialism, because the government lays down explicit rules on how owners can use “their” property. Indeed, the term Nazi itself stands for National Socialism. The communists tended to be more concerned with international class struggle, whereas the fascists were more concerned with the strength of their individual nations.
When it comes to evaluating the fruits of various ideologies, therefore, the horrors of both communism and fascism can be laid at the feet of socialism. Say what you will about the inequalities of a pure market economy, the Holocaust would not have been possible in a society where private property rights were sacrosanct. Wise political thinkers have always warned that if rulers have the power to do great good, they simultaneously have the power to do great harm.