But a sauce pan has straight sides. Even if you specify that you mean a frying pan, there is no universal difference. The choice of which word is more commonly used, and any differences between the meaning of the two, are merely a matter of regional usage.
A saucepan is actually a pot ... however, I'm using my knowledge from when I went to culinary school to become a chef ... I do agree that there can be differing answers based on region.
Skillet is the flat silver metal thing that you can cook on without a pan and a pan is what you have to use on a stove.
A skillet has straight sides and often accompanies a lid, whereas a pan has sloping sides.
Actually, that's a griddle.