Pans are measured according to the diameter of the lip, not the diameter of the cooking surface. Most home burners can only comfortably fit a pan of around 12 inches in diameter. Because of its straight sides, a 12-inch sauté pan will also have a large, 12-inch-wide cooking surface (about 113 square inches). A skillet, on the other hand, loses at least an inch on each side, making the effective cooking area only 10 inches wide (about 79 square inches). This means that, given a skillet and a sauté pan of equal diameter, the skillet will have 30% less cooking area than the sauté pan. That's not an insignificant amount.
The quick answer is, no. A skillet and frying pan are different because of each’s cooking surface and design. There is often confusion because the terms “skillet” and “frying pan” are often used interchangeably. And you can typically use either one of them for many cooking preparations, even if one is better suited for a specific cooking method. Plus, both of these style pans are often made from the same materials and come in similar sizes, so it's easy to understand why there can be confusion. While similar, a skillet is technically a bit deeper and has a slightly larger cooking surface area than a frying pan.