I think the topic was pretty thoroughly dealt with on another thread in the past couple of years.
There is no genetic difference between sorrel and chestnut; sorrel is a regional term for some shades of chestnut, and may be defined somewhat differently in different places. In North America it tends to be associated with the western horse breeds along with other color words with Spanish origins.
Just like there is no genetic difference between a piebald and a black tobiano pinto.
I have read that the higher rate of unusual colors in the American horse population is due to the fact that during the era of the Spanish Conquest of Mexico, crazy color horses that had previously been popular were now out of fashion in Spain. So they got shipped to the Americas.
I also suspect there is a camouflage survival advantage for feral horses in being palomino or buckskin especially in arid country and also in being parti-colored (pintos and Appaloosas). The frame Overo pattern actually apparently was a mutation in horses of Spanish descent in the Americas. My chestnut Frame Overo mare can momentarily disappear in a turn out arena with patches of snow in the flat grey winter light.
The creme and dun dilutions and various pinto patterns are relatively common in feral horse populations that have Spanish origins (mustangs) and this stock contributed to the development of the American breeds historically.
