WRONG! Hitler in his speeches time and time again talked about removing classes from German society.
The only difference between Nazis and Communists was that the Nazis had snappier uniforms.
The Nazis did not confiscate and nationalize private property (at least not the property of non-Jewish Germans). Hitler had the backing of bankers, industrialists, and aristocratic landowners because regardless of what liberties they lost under his rule, they would at least be able to keep their land and wealth under the Nazis. Far from having their property nationalized, many industrialists like Krupp and Porsche became filthy rich thanks to government contracts. The communists would have seized the property and probably would have killed people like Krupp and Porsche, as happened in Russia.
In other words, private individuals could own businesses and land in Nazi Germany or Fascist Italy. They couldn't in Communist Russia.