The term Parmesan may refer to either Parmigiano-Reggiano or, when outside the European Union and Lisbon Agreement countries, a locally produced analog

The names Parmigiano Reggiano and Parmesan are protected designations of origin (PDO) for cheeses produced in these provinces under Italian and European law. Outside the EU, the name Parmesan is legally used for imitations, with only the full Italian name unambiguously referring to PDO Parmigiano Reggiano. A 2021 press release by the Italian farmer-rancher association Coldiretti reported that, in the United States, 90% of “Italian sounding” cheese sold as parmesan, mozzarella, grana, and gorgonzola was produced domestically.

In many areas outside Europe the name Parmesan has become genericised and may denote any of several hard Italian-style grating types of cheese. These cheeses, chiefly from the US and Argentina, are often sold under names intended to evoke the original, such as Parmesan, Parmigiana, Parmesana, Parmabon, Real Parma, Parmezan, or Parmezano.

From the same Wikipedia article