OK, you know what a grater is and have been using one all your life, but there are dozens of types on the market and most of them have at least two, and sometimes as many as eight, surfaces.
Grating creates fine threads by passing the ingredient over a serrated surface. The basic grater is a flat piece of metal with notches cut in its face and it is the size of the notch that determines the size of the threads.
Shredded food is usually thought of as being a larger, coarse thread while grating creates a finer one (that can even be as fine as powder). Shredded cheese will melt much slower than grated cheese by virtue of the difference in surface area between a coarse and fine thread. For a recipe like Philly Cheese Steak, I prefer to use cheese that has been finely grated. For a recipe where the cheese should melt slowly – on top of a casserole for instance – use shredded cheese.
There are a dizzying amount of choices of graters available. The basic 4 sided box grater is an essential kitchen tool. The one that I have has a face for fine shredding and coarse shredding. There is a face for both coarse and fine grating as well. Many box graters will have a face that cuts thin slices but I have never found this to be very effective.
I grate all hard cheeses in a rotary grater. Mine is a Zyliss and was a gift from an old medical school friend. The fine serrations are on a drum that rotates on a crank while you push the cheese into the hopper with a hinged plunger. This is one of the finest luxuries that I know of and should be one of your first kitchen purchases. There are a number of manufacturers and many offer different drums that grate from fine to very coarse.