Genetically, sorrel and chestnut are exactly the same from what we currently know. There may very well be some variant in there that changes the shade, but as far as what is known right now, they are the same color, just different names. Sorrel is typically only used in stock breeds.
I feel there is a slight difference in sorrel and chestnut. In my opinion, and it has been mentioned already sorrel is more "orange" with a lighter mane and tail, where chestnut is dark red with a dark mane and tail. My gelding is a chestnut, even his face is darker then the rest if his body and his mane and tail have more brown and black mixed in.
Except according to AQHA both sorrel and Chestnut can have flaxen manes and tails. So there goes the darker mane theory.
Sorrel & chestnut are Basicaly the same.
People just have there Prefrence on which they call sorrel & chestnut.
I always called the redder darker shades with the same reddish mane Chestnuts
& I always call the Chestnuts with Flaxen manes Sorrels.