To be simple… Look at politics as a square.
The top side of the square is 100% government control and authority. The bottom being 0%
The left hand side of the square is essentially 100% tax. The right being 0%.
Depending on policy, different groups find themselves at different coordinates in the square.
To answer the original posters question - Communists and Fascists essentially exert the same amount of authority. But differ in their economic policies. IE one could be rich in Nazi Germany, where as in communism, the economic freedoms were not as available. That is one of several conclusions that leads people to see the Nazi’s as right wing.
In simpler terms it’s “Government control of business (Left) vs Business control of Government (Right).”
But is that enough to make the NSDAP a right wing party? In my opinion no. As I feel that all big government is essentially “Left Leaning/Socialistic”. Meaning that 3/4 of the square is socialism (Anything with more than 50% authority, or 50% tax control of your life)
Again, a very rudimentary and simple perspective, take it or leave it.