Are there clear affinities of Communism with Fascism?

Political philosopher John N. Gray on liberals' totalitarian temptation
Times Literary Supplement, Jan 02, 2013:

One of the features that distinguished Bolshevism from Tsarism was the insistence of Lenin and his followers on the need for a complete overhaul of society. Old-fashioned despots may modernize in piecemeal fashion if doing so seems necessary to maintain their power, but they do not aim at remaking society on a new model, still less at fashioning a new type of humanity. Communist regimes engaged in mass killing in order to achieve these transformations, and paradoxically it is this essentially totalitarian ambition that has appealed to liberals. Here as elsewhere, the commonplace distinction between utopianism and meliorism is less than fundamental. In its predominant forms, liberalism has been in recent times a version of the religion of humanity, and with rare exceptions— [Bertrand] Russell is one of the few that come to mind—liberals have seen the Communist experiment as a hyperbolic expression of their own project of improvement; if the experiment failed, its casualties were incurred for the sake of a progressive cause. To think otherwise—to admit the possibility that the millions who were judged to be less than fully human suffered and died for nothing—would be to question the idea that history is a story of continuing human advance, which for liberals today is an article of faith. That is why, despite all evidence to the contrary, so many of them continue to deny Communism's clear affinities with Fascism. Blindness to the true nature of Communism is an inability to accept that radical evil can come from the pursuit of progress.

John Gray is professor emeritus at the London School of Economics