For many people, the thing you fry things in on a stovetop is called a "frying pan." This, however, isn't what the stores call them. Needless to say, this can lead to some confusion when it's time to buy this type of cookware. If you go ahead and buy a 10-piece cookware set, it'll come with two or three good frying pans and you won't have to worry about the details. If you just want to buy one or two, though, it's a good idea to be sure of the specifics.
The type of pan that is used for most stovetop shallow-frying is actually called a skillet. Skillets have a large bottom surface area, but they also have fairly high sides. The high sides allow you to cook things like stir-fries, loose vegetables, and other such foods without worrying about the ingredients slipping out onto the stovetop or the floor.
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A griddle, on the other hand, has an even bigger bottom surface area relative to the sides. The sides themselves are either very short or nonexistent. Griddles come in two main forms: Those that fit over the burners of the range, and those that have handles much like skillets do. Burner-oriented griddles usually have no sides, while handled ones tend to have the short sides. Having even short sides helps prevent food spillage, but it will also make it so you can't get a direct shot at your food with a pancake turner. Which one you prefer will likely be more of a matter of preference than actual functionality.
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Other types of frying pans can be even more specialized. There are ones made specifically for frying single eggs, making crepes, and cooking omelettes. These unique varieties are available from Amazon.