The difference between a sauté pan and a skillet all comes down to shape. A sauté pan, from the French verb meaning "to jump", has a wide, flat bottom and vertical sides. A skillet, on the other hand, has sides that flare outward at an angle.
Again, the straight sides of a sauté pan allow you to fit a higher volume of liquid into the same amount of oven space. Straight sides also make the liquid less likely to splash out as you move the pan around or transfer it into and out of the oven. It also allows the lid to fit more tightly, minimizing evaporation. This extra volume is a great boon when you're performing tasks like shallow-frying a pan full of meatballs in a half inch of oil, or braising a dozen chicken thighs in white wine.
A skillet offers advantages for sautéing, and a sauté pan offers advantages for shallow-frying, moderate-temperature searing (as for chicken pieces), or braising.