"Left" and "Right" refer most properly to the sides of the aisle at the National Constituent Assembly during the French Revolution. Since then they have been plastic terms that very broadly refer to the relationships between what has become termed "progressive" and "conservative" which in turn are terms entirely relative to whatever status quo is being changed or preserved, respectively, at the moment. In short, it means pretty much what the speaker and the context dictate, or in other words not a great deal when universals are requested, which is what you've done.
Did the Nazi ideological drive incorporate populist social elements? Absolutely. In that sense it could be described as "left-wing." Did it differentiate itself from the strict economic definition of socialism? Yes, it did. It also differentiated itself from the strict economic definition of fascism as well, at least as Mussolini described it shortly before Hitler came into power.
In the communist interpretation of socialism the State takes ownership of the means of production and dictates what Marx clumsily termed the relations of production. Under Nazi fascism the State allowed private ownership of the means of production as long as it controlled its usage; in Marxian terms also dictating the relations of production. These two economic systems were similar in that both of them enslaved the very workers they were ostensibly created to protect.
In terms of utopian aims the two systems were also just similar enough to be deadly enemies. Nazism proposed the accession of a specific Master Race. Communism proposed the accession of a specific economic class, the Proletariat, who were in strict Marxian terms present absolutely nowhere by the time their respective systems came into conflict. (Arguably, neither was the largely fictive Aryan race).
The translation of this form of "Left" and "Right" already is far departed from its inception during the French Revolution and the associated Enlightenment. We've come a full half century from then. It should be little surprise that those terms are even less accurately applicable today.
You must be using a unique calendar.
Thank you, Bill. You probably aren’t going to believe that my undergraduate degree from a major university was in Political Science, yet I never read about the aisles at the National Constituent Assembly! I can’t help but agree with so many of the posters here who seem to be saying that “left” and “right” have drifted far away from their original meanings, and that their use in political discourse is either confusing or intentionally ambiguous. Are we DOOMED to political discourse that uses terms no one understands or agrees on? Is this a good idea, as the world becomes more contentious and dangerous?