The original ones, in Germany. It was short for "national socialist" - that is literally where "Nazi" comes from. They were different from the communists in that they were national rather than international socialists.

At least, that's what it said on the tin. Not sure, once they got into power, how actually socialist they were. (On the other hand, once the communists got into power, I'm not sure how communist they actually were.)

I mean, they claimed to be. It was in the name, "Nazi" was a contraction of "National Socialists". But that's kind of the problem with much of these conversations online. They figure way too much on the naming of things and not enough on the outcomes of things. I think anyone with an honest understanding of the Nazi party would admit it was much, much more about the "Nationalism" then it ever intended to be about the "Socialism". Much like how the modern "Republican" party doesn't seem to care too much about republics.