These are both true in, at most, the same sense that it is true that North Korea is a democratic republic.
Anyway this is why Nazis while mainly being far right managed to gather supporters from the far left. And especially in the beginning there where decision done which looked quite socialist, through in retrospective where basically always ware preparations.
I would say saying Nazis where socialists is quite wrong, but that doesn't mean there wasn't a bit of socialism their politics eve if just for pretentious reasons.
Through it also should be noted that the current political spectrum differs quite a bit from back then, neo-nazies normally have very clearly nothing to do with socialist and the far left has not many people which are extreme socialists but also nationalist either as far as I know.