Knowing the brand of cheese and serving size would be helpful. Can't you simply read the nutrition label on the package?
Well, first the Mozzarella (italian) is buffalo cheese (with high water content). There's no "swiss cheese" - there are a lot of different ones from Switzerland. They are mainly produced with cow...
Grated and shredded are terms used interchangeably when referring to cheese. They mean the same thing.
a kind of cheese that has a number of holes in it