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?