The principal distinctive between Nazism/fascism and Communism/socialism was that the former was ethnically centered and nationalistic while the latter was universalist and internationalist. This distinctive reflects the roots of the political philosophies. Naziism drew in part from the 19th Century Romantic reaction against the rationalism and individualism of the 18th Century. As opposed to the notions of the autonomous individual, Naziism sought the meaning of existence in the national or racial collective. It also drew from the concepts of the Superman and the will to power of the German philosopher Freidrich Nietzsche. These notions, remarkably similar in effect to the Leninist theory of the vanguard of the proletariat, called for a strong leader to defy conventional morality and individual rights for an overarching goal, which in the case of the Nazis was the greater glory of Germany and the supremacy of the Nordic or Aryan "race." It also led to the glorification of a god-like Fuhrer or Duce who was above the law or even conventional morality. The Nazis called it the Fuhrerprinzip.
Unlike Naziism, Marxism-Leninism did not reject the rationalist viewpoint, at least in its materialism. Rather, it utlized the concepts of evolution popularized by Darwin in biology to promote the concept of a social evolution of the human race from barbarism through feudalism and capitalism to the ultimate end of that evolution, communism, defined as the universal ownership of all goods by all people and the end of class distinctives and of civil government. Marx conceived of this evolution occuring in class struggle between the bourgeoisie and the proletariat. He also rejected certain aspects of rationalism, accepting the critiques of German philosophers Kant and Hegel. From Hegel, Marx adopted the theory of the dialectic (thesis plus antithesis leading to a third position, synthesis) as the main mechanism of change in the universe. Lenin refined Marxian class struggle theory to propose the need for a revolutionary vanguard, the Communist Party, that would lead the proletarians in violent revolution. This elite, like its Nazi/fascist counterpart, could justifiably violate ethical rules and individual rights, but to accomplish the historical process of evolution to communism and not to glorify a nation, race, or supreme leader.
Naziism and other fascist or authoritarian governments condemned the extremes of total state ownership, as in the USSR, and laissez faire capitalism, as in America before Franklin Roosevelt. Nazi economics were dirigist, that is, maintainance of private ownership, but under strong state supervision, as well as state monopolies over education, utilities, and transport. In essence, it was a earlier version of Third Way economics advocated by the present day European social democratic parties. The New Deal was a modified version of the corporate state concepts of Mussolini, especially the National Recovery Administration, with its committees of labor, management, and government closely resembling Italian Fascist models. Many of the criticisms of both free market economics and state socialism can be found in Papal encyclicals, such as Rerum Novarum in the 1890s and in the writings of British traditionalist Catholic philosophers such as Hilaire Belloc and G. K. Chesterton. American populists like Tom Watson and William Jennings Bryan also favored a sort of "Third Way" via large scale government intervention, as did Progressives like Theodore Roosevelt and Woodrow Wilson.
In America, our "throne and altar" are the Constitution and the Bill of Rights. American tradition is one that exalts individual rights as being God-given and inalienable. Religion, the press, and commerce are to be left alone. If the "Right" is, in the American context, support for our traditions of limited government, personal freedoms, and private property, Naziism/fascism, Communism/socialism, and modern liberalism are all on the "Left." In the American context, not only are John Reed, Abbie Hoffman, and Norman Thomas men of the Left, but so are David Duke, Huey Long, and Charles Coughlin, as well as Bill Clinton, Franklin Roosevelt, and (yes) Richard Nixon.
The LUFTWAFFE trained secretly in USSR in the mid thirties to circumvent the WWI disarmament accords.
There were EXTENSIVE interchange programs between the Wehrmacht and the Soviet Army.
Many believe the Jewish Holocaust was inspired by Soviets (along with the Turkish genocide of the Armenians)when the Germans observed how world opinion ignored the Soviet Pogroms and in particular, the state run starvation of the kulak -- the Ukranian Holocaust where millions died.