Just because it shares the same name that does not mean it is the same thing, I can't see why this is so hard to comprehend.

It's like saying to row a boat is the same thing as a series of horizontal of items in a row because they hold the same name.

In DemSoc, SocDem, and other iterations of classical socialism things are based on a derivative of Marxist socialism where ownership of the means of production, and an attempt at abolition of classes.

National Socialism is a derivative of Fascism which contrary to your misconception is not to do with socialism as a derivative, only a means to counter it. Fascism and NatSoc were derived from Sorelianism which developed in tandem but with different aims and we're results of enlightenment thinking as an alternative to reactionary thinking when considering a response to socialism, and capitalism of an ultra-libertarian kind. NatSoc's economic and other ideals were in many ways based on corporatism where instead of abolishing government and/or class, there would be inter-group and in-group collaboration between state, classes and hierarchies both new and traditional. 

To review: Left-Socialism seeks to abolish most hierarchies and has ultra-collectivist economics and has an attempt at removal of capital/currency or at least limiting it's significance, as well as removing the extraction of excess value. 

In NatSoc, corporations exist and have an important role. Capital still exists, and there is no collectivism, even if there are typically rather large taxes typically found in national socialist systems. 


Trying to say national socialism is socialist is only a result of either stubbornness in the face of the obvious or lack of education on the matter, you seeming to suffer a bit of both, despite general reasonableness and being generally knowledgeable.