That's called branding. The name was chosen to be appealing to the German people, not to be an accurate description of their form of government. Unless you think North Korea (official name "Democratic People's Republic of Korea") is actually a democratic republic, this should not be a difficult concept to understand.
Right, because National Socialism was a system in which a dictator for life ran a single party system running a command economy and police state, with systematic persecution of minorities and dissenters, while Russian Communism in contrast was... er... completely different than that... somehow.
I mean that article goes on and on about how anti-Marxist the Nazis were. They essentially claimed that they were the "true" socialist and Marxists weren't. Much like how North Korea would probably say that they are the true democracy and everyone else isn't.
> Our adopted term 'Socialist' has nothing to do with Marxist Socialism. Marxism is anti-property; true Socialism is not
> The Nazis claimed that communism was dangerous to the well-being of nations because of its intention to dissolve private property, its support of class conflict, its aggression against the middle class, its hostility towards small business and its atheism.[205] Nazism rejected class conflict-based socialism and economic egalitarianism, favouring instead a stratified economy with social classes based on merit and talent, retaining private property and the creation of national solidarity that transcends class distinction.
So they did have their own definition of "socialism" that they met, but that definition had virtually nothing in common with the way that the rest of the world defines it.
I always found it funny they call it far right.