Hmmmm........ I had always heard that a shallow straight-sided pan was a sauté pan and the shallow sloped-sided one was a fry pan/skillet. https://www.thekitchn.com/whats-the-difference-saut-pan-87524
The difference of use is in the name of the sauté pan (sauter = "to jump" in French). The sloped sides of this type of pan facilitates this cooking technique.
Go to 1:15 in this video:
https://www.youtube.com/watch?v=CTyV3JExDT8
The sloped side of the sauté pan helps with this motion. It is difficult or often impossible to do with a skillet with straight sides.
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Go to 1:15 in this video:
https://www.youtube.com/watch?v=CTyV3JExDT8
The sloped side of the sauté pan helps with this motion. It is difficult or often impossible to do with a skillet with straight sides.