National socialism is nationalism on steroids, with the word "socialism" intentionally slapped on top to make it look like something it isn't.
Is a Chevy Vega GT a real GT high performance car?
Heh, maybe if you're racing a four year old on his plastic Big Wheel trike.
Oh wait, those aren't four year olds...
But I bet they still could beat a Chevy Vega GT.
And GM convinced enough buyers that it really was sporty that they didn't lose their ass on the car...until they did.
Never mind that the zero to sixty time was measured in months, not seconds.
And that's about what "National Socialism" is to SOCIALISM.
It's a "GT" sticker to make people think it is something it's not, because in 1930's Europe, the word "socialism" sounded pretty good to most Euros, particularly the Weimar weary debt addled Germans who were, at the time, burning large bundles of Reichsmarks because it was cheaper than buying firewood.
National socialism is just fascism with an attractive sounding name.
But it is indeed true that both nazism and pure state socialism are authoritarian in nature.
Social democracy, on the other hand, is capitalism.
It's capitalism done the FDR way, the New Deal way, pretty much.
Thing is, FDR was smart enough to sell it as a very American and very middle class friendly form of capitalism, and he never mentioned the word "socialism" or "social".
He just added the hot sauce and everyone's capitalism tasted a little better, that's all. He didn't even get to add enough of the stuff, but it still helped a great deal.
It helped for well over forty years.