Graters and shredders differ only in title, not function. You usually find coarse-grated cheeses, such as packaged mozzarella for pizza, labeled "shredded," and fine-grated cheese, such as Parmesan, labeled "grated," but it's just semantics. The type of grater you use for what ingredients is what's important.
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Grating and Shredding Tools
There are hundreds of types of graters labeled for use with foods as diverse as carrots, nutmeg, soft cheeses, hard cheeses, truffles and even chocolate. Yet all graters, regardless of the food they're used on, perform the same function -- they simply vary in blade size. You can divide graters into three main types: fine-bladed, coarse-bladed and ribbon-style. Fine-bladed graters work best for ingredients where a little goes a long way, such as hard cheeses like Parmesan and pungent alliums like garlic. Coarse-bladed graters make short work of hard vegetables, such as carrots and potatoes, and soft cheeses, such as Monterey Jack and cheddar. Ribbon-style graters, which look like woodworking rasps, shave ingredients into ethereal wisps, just what you need for delicate ingredients, such as lemon zest and truffles.