If both pans are the same size, the frying/sauté pan will have a slightly larger surface area. In a 12-inch diameter pan, it can make the difference when fitting in pieces of chicken or other food, so you can cook everything in one batch.
The other benefits of a frying/sauté pan: Liquids are less likely to splash out of the higher, straight sides; and lids fit more tightly, limiting evaporation.
Chefs prefer the sloping sides of a skillet for quick cooking techniques like stir-frying, where the ingredients need to be moved around continuously. A skillet is also a better option for a frittata, served straight from the pan.
It is a fun fact in cooking that a skillet is better for sautéeing than a sauté pan. The sloping sides make it easier to move pieces of food around while constantly stirring, and to more easily shake the pan to toss the food for even cooking. For the best sear, choose a cast iron skillet. It gets hotter than other metals.
You can, of course, sauté your food in a straight-sided sauté pan, but it requires more work: constant stirring and turning.
Guessing that the straight-sided frying pan may have come first, and the skillet adapted for greater flexibility, we tried to locate the facts. What we found was this, in Wikipedia:
Before the introduction of the kitchen stove in the mid-19th century, a commonly used cast iron cooking pan called a spider had a handle and three legs used to stand up in the coals and ashes of the fire. Cooking pots and pans with legless, flat bottoms were designed when cooking stoves became popular; this period of the late 19th century saw the introduction of the flat cast iron skillet.
Professionals use a sauteuse (saw-TOOZ), a pan that combines the best higher sides of the sauté pan and the sloping sides of the skillet. It is also called a fait-tout (fay-TOOT), which literally means that it “does everything”.”
Finally, mention must be made of the grill pan. It’s a frying pan with very low sides and series of parallel ridges on the cooking surface, which both enables cooking with radiant heat like a grill, and allows the fat to drain down.
THE HISTORY OF PRETZELS
It was all for the kids. In 610 C.E., monks in the what is today southern France northern Italy twisted and baked scraps of dough as a reward for children who had memorized their Bible verses and prayers.
The shape represented the monks’ concept of a child’s arms folded in prayer. The monks called this soft, baked dough a “pretiola,” Latin for “little reward.”
The word evolved into the Italian “brachiola,” which means “little arms.” Over the next few centuries, the pretiola journeyed through the French and Italian wine regions, crossed the Alps, traveled through Austria and arrived in Germany, where it became known as the Bretzel or Pretzel.
Here’s more of pretzel history.