There is a long quote from Hayek that applies here:
“Although our modern socialists’ promise of greater freedom is genuine and sincere, in recent years observer after observer has been impressed by the unforeseen consequences of socialism, the extraordinary similarity in many respects of the conditions under “communism” and “fascism.” As the writer Peter Drucker expressed it in 1939, “the complete collapse of the belief in the attainability of freedom and equality through Marxism has forced Russia to travel the same road toward a totalitarian society of un-freedom and inequality which Germany has been following. Not that communism and fascism are essentially the same. Fascism is the stage reached after communism has proved an illusion, and it has proved as much an illusion in Russia as in pre-Hitler Germany.”
“No less significant is the intellectual outlook of the rank and file in the communist and fascist movements in Germany before 1933. The relative ease with which a young communist could be converted into a Nazi or vice versa was well known, best of all to the propagandists of the two parties. The communists and Nazis clashed more frequently with each other than with other parties simply because they competed for the same type of mind and reserved for each other the hatred of the heretic. Their practice showed how closely they are related. To both, the real enemy, the man with whom they had nothing in common, was the liberal of the old type. While to the Nazi the communist and to the communist the Nazi, and to both the socialist, are potential recruits made of the right timber, they both know that there can be no compromise between them and those who really believe in individual freedom.”
— F.A. Hayek, The Road to Serfdom
Yes. Both Hitler and Mussolini were always “men of the left”. It was widely known at the time. But both saw international socialism as not working. They believed they could obtain better results with national socialism.
That is the big difference between communism and fascism. One promotes international socialism, the other national socialism.
Hitler rejected communism, in large part, because of a failed revolutionary attempt while he was part of the Bavarian Soviet Republic. Anayzing the defeat, he realized all the leadership of his failed party were Jews! Then he came to the conclusion that Jews were the reason for the failure.