
Whether you’re upgrading your kitchen tools or pretending to be a gourmet chef for your next undercover assignment, understanding the distinction between a skillet and a sauté pan is essential. Thankfully, it’s quite simple to grasp.
As Business Insider

Thanks to its straight sides, a sauté pan can accommodate more liquid without the risk of spills onto your stove (or your feet), unlike a skillet. If you’re working with large amounts of sauce, wine, oil, or any other liquid that could easily splash, a sauté pan is the better choice.
Skillets, on the other hand, have their own advantages. As noted by J. Kenji López-Alt, Serious Eats’s chief culinary consultant, the smaller base of a skillet makes it lighter and easier to handle with one hand. The sloped sides are ideal for flipping food like a professional, promoting even cooking. Ironically, skillets are better suited for sautéing than sauté pans.
If space (in your kitchen or budget) is limited and you can only have one shallow pan, López-Alt suggests opting for a skillet, as sautéing is a frequent step in many recipes.