Let’s start with a language lesson: Grana is a style of hard, salty cheese, typically made in Italy, that you might use to grate over pasta or eat by the chunk. Parmigiano-Reggiano is a type of grana cheese made according to strict regulations, and only in five provinces around Italy’s Po River Valley. The producers of Parmigiano-Reggiano are members of the Parmigiano Reggiano Consortium.
And Parmesan, the term most of us put on our shopping lists, is a word these Italian cheesemakers would like to erase from the American vocabulary. You’re right to be confused. I too have spent my life colloquially referring to everything from the cheese I ate in Parma itself to the Kraft stuff that comes pre-grated in a canister as “Parmesan.”