If you take your time to go through nazi material and meeting minutes, they called themselves socialists at all times and they implemented socialist policies at all times. National socialist policies.

There is absolutely no doubt on this, and there are volumes upon volumes of backing this in the written evidence collected by the allies for the Nuremberg trials. They outwards called themselves socialists in their propaganda. They called themselves socialists in the laws and decrees they issued. And they called themselves socialists in their internal meetings between top nazis, long after they had assumed all power. It wasn't just rhetoric or propaganda, it was the real deal.

And if you consider the kind of policies and program implemented, they were socialist in every aspect, and the German citizen had their life completely organized in socialism. From the cradle to the grave.

But they certainly weren't socialist in the shape or form that present day socialists are.

You can be socialist without being a leftist or a liberal. You can be a socialist while having communists as your main enemy. You can be a nationalist or not while being a socialist or a conservative. National socialism became the de-facto system of government for both the Soviet Union and for China.