Actually, there is only a difference in terms. Most fresh mozzarella is made from whole milk, is never aged and comes either water-packed or cryovacked. And of course, if you want, you can shred it. The easiest way to shred fresh mozzarella is by using a box grater. Shredded mozzarella is always made from a low-moisture cheese, and usually has sulfites and anti-caking agents added to improve shelf-life usability. The differences in taste between the two are many. Fresh mozzarella is moist, delicate and has the distinct ability from all cheeses to go with many different dishes.