Communism is the theoretical result of marxist socialism. The Lenin quote is correct from a marxist perspective in that the goal of socialism should be communism, a classless, stateless, egalitarian society.
National Socialism wasn’t socialist in the common sense moreso it was based on a “socialism of duty” intertwined with collectivist thought in that man should work for the good of society collectivley. National socialism was racially nordicist but nothing about it was about “racial cleansing” beleiving in the superiority of or inferiority of a race doesn’t classify as racial cleansi