Sauté pans, skillets and frying pans are all basically the same thing; a round, flat, shallow pan. The word sauté means to jump, and the sauté pan has a slanted lip designed to keep the food moving. With a flick of the wrist a trained chef can keep the food jumping all day. If your wrist muscles are not fully developed, you can stir with a spoon to obtain the same results. Whenever you see the term sauté, it is an indication that the food is meant to be stirred around in the pan throughout the cooking process. The large surface area of this pan promotes quick, even browning.
A skillet usually refers to a heavier pan, often cast iron. The side of the pan is straight, designed to hold fat for frying. Skillets are typically used for prolonged pan-frying or deep-fat frying. In French culinary arts, a wide, shallow, straight-sided pan is called a sauteuse.
Saucepans are round pans with tall sides and, typically, one long handle. They are designed for simmering or boiling large amounts of liquids, and are called for in recipes for sauces, soups, stocks, boiling vegetables and grains. They are usually identified by quart capacity, but in general, a well equipped kitchen should have a small, medium and large saucepan.
A larger pan, with a capacity of one gallon or more is generally called a stock pot. The long handle has been replaced with two short handles for easy lifting. A pasta pot is a small stock pot, usually with a colander insert, which makes draining the pasta a snap.
Recipes generally indicated when a pan should be non-stick, cast-iron, or simply heavy. Non-stick is preferable for most egg cookery, and delicate frying that would be ruined by the food sticking, like dainty fish filets. Cast iron is suggested for most deep-frying because it holds the heat well, distributes it evenly, and is so heavy that it is difficult to accidentally tip it over. A heavy pan should be aluminum or have an aluminum core. Aluminum heats slowly and evenly, and does not allow scorching. I rarely suggest stainless steel, as it heats too quickly, and burns easily.
When using a non-stick pan, be sure to use a heat-resistant plastic spatula. Flipping food in a non-stick pan with a metal tool scrapes off the non-stick surface. It is also important to clean a non-stick pan carefully. Use a brush or sponge, never a scrubby or scouring pad.