Nazis named themselves socialists and political right oriented, so that is a fact for sure. 
And I agree often we have to find terms we can use as a reference to describe complex ideas. 

Anyhow these terms are often used in a lot of different situations and often pushed into a new framing for „marketing“ without being specific.

That’s why these terms alone are imo not „ideal“ for describing things. You always need to add information or references to explain what you really mean.

E.G. terms like „socialism is is the opposite of right“ (what is often the current political situation) and „extreme right is socialism“ (what was the situation for political parties in the „Deutsche Reich“) are both wrong in general, but can be useful if you add the specific context.