Nazi is a contraction of the German name of the National Socialist German Workingmen’s Party. They were, plain and simple, SOCIALISTS above all else, and as such, have few doctrinal differences with any other socialist ideology in the world (including Islam, by the way).
Command and control regimes all end up with the same general traits and priorities. Total conformity to the demands of the elite few at the top, with infractions to be punished most severely, and the enforcement carried out on a servile, but uninspired, multitude, with the force of threats of death by a well-armed and largely unaccountable secret police force.
Of course, those doctrinal differences between various flavors of socialist regimes are enough for the parties involved to go to war with each other, as each believes there is only one True Path to the pure socialist state, and error must be purged.
At all costs, including mutual destruction.
When I was home schooled I read “The Rise And Fall Of The Third Reich” and had to write a paper on it; however, when you start applying the term Nazi to someone you’re incorporating all the evil behind that name on that person you’re calling a Nazi.