Parmesan is a cow's milk cheese that is aged for at least a year or longer, while Pecorino Romano is a sheep's milk cheese that is aged for a shorter period.
The cheeses have a similar texture and appearance, but parmesan has a sweet, nutty taste with a strong umami backbone, while Pecorino Romano has a saltier zesty and grassy flavor.
You can use parmesan and Pecorino Romano interchangeably. However, each cheese will impart a slightly different flavor, and you must adjust your recipe to accommodate this.
Pecorino Romano is saltier than parmesan, so adjust the salt depending on the substitution. Also, mind salty ingredients like anchovies, and perhaps dial those back.
Pecorino Romano works better in dishes with strong flavors that might overpower parmesan and is also worth tracking down to make a classic basil pesto.
Both cheeses are great for topping vegetable dishes, pastas, salads, and pizza, and both have thick rinds that can be added to soup to make a rich vegetarian stock.