What's a National Socialist?

I'm a little confused about what polices make national socialism and about the terminology of the name.  In the USA it seems that political terminology is different than in other parts of the world.  A lot of people here say that left vs right=statism vs anarchism.  I thought that left vs right=radical change/progressivism vs status quo/traditional values.  The fact that the title national socialism includes the word "socialism" and that it was very statist, a lot of people in the US say that the Nazis were left wing.  This confuses me because they hated communists and trade unions, and because Mussolini described fascism as being when state interests were the same as corporate interests.  So much so that fascism could also be called corporatism.  That desn't sound left wing to me.  It also seems that left wing movements tend to be communal such as communists believing that national borders should be disssolved while right wing movements tend to me nationalistic.  This also does not fit the Nazis being left wing.  So are national socialists left or right wing?  If right, then where does the "socialist" in national socialist come from?

>>5

You're not realizing that socialists can be of the right wing. Under socialism, capital is publicly owned and operated, and the fruits of labor applied via this capital flows "from each according to his abilities, to each according to his deeds." How what does or doesn't constitute deeds of quantifiable merit is somewhat arbitrary, but one approach is to simply let each socialist worker bear the fruits of his/her labor, or the monetary equivalent in proportion to the worker's output.

The catch is that the private capital of undesirables was being seized and confiscated by the state (the federation), under the Third Reich. Availing this capital for public use with no intention of transferability is socialism; whereas auctioning it off to the highest private bidder, or selling it, in whole or in part (as stock), to private buyers is capitalistic if not capitalism. In so far as the NSDAP was socialistic, then the option former was favored over the option latter.

Understood?