Reggiano Parmigiano

Martha Stewart, in her macaroni and cheese recipe, includes this ingredient:

2 ounces Parmigiano-Reggiano cheese, grated (1 cup)

So 1 Cup of grated Parmigiano Reggiano is equal to 2 ounces.

Parmigiano reggiano is Parmesan cheese in English. This kind of cheese is a hard, granular cheese. It is cooked, not pressed and is named after the producing areas near Parma.

Parmesan is and is not the same as Parmigiano.

Parmesan cheese is a term commonly applied for commercial purposes outside of Italy to Parmigiano Reggiano cheese, one of Italy's finest.

Parmigiano Reggiano is a DOP product which means it is protected by European Law and only the cheese made from the zone of Parma and nearby can be classed as the real thing.

Parmesan cheese is, therefore, a cheap imitation.

Usually a hard cheese. You probably mean parmesan (parmigiano-reggiano) but you can also grate pecorino romano, grana padano, etc...