The words are just labels. Marx pictured communism as the a social situation in which the State has withered away and people just share stuff.
But people say Lenin and Stalin established communism in the Soviet Union. The State did not wither away in the USSR.
People use words to mean a lot of different things. Based on sloppy human usage over more than a century, I cannot really tell you what communism is, or socialism is, or what fascism is.
What I can say is: all collectivist systems are Left-wing.
Social systems emphasizing individual freedom are Right-wing.
“Based on sloppy human usage over more than a century, I cannot really tell you what communism is, or socialism is, or what fascism is.”
You have some point there, a great mixture of sloppy human usage, to the point of utter confusion, resulting in the situation where one gets people actually believing that a Communist and a Fascist have no real differences.
The "Führerprinzip" (leader principle) was the core of the Nazi movement. It holds that "Führer" (leader) is above all law and is the supreme leader of all legislation, policy, and military decisions.
Hitler and party leaders were extremely anti-communist. The communists were blamed for the '33 Reichstag fire and prompted arrests of communist party leaders.
You are spot on that anti-communist does not mean pro-democracy. Hitler's position of anti-communism/pro-facism demonstrates this. Neither movement supports individual rights and both work to increase the power of the state.