I found these on the AQHA website. Personally I would say that a chestnut has a darker mane and tail than their body color and a sorrel is the same all around or else a lighter mane and tail. But the 3rd and last picture don't agree with me so I'm probably wrong.
Red – chestnut or sorrel – is a recessive trait.
The color is caused by pheomelanin
(fee-oh-MEL-ah-nin). This sorrel is
Higher Math, owned by Julianna Hawn Holt
Of Blanco, Texas.
These two horses are the same genetic color, but are different
Shades. The horse on the left is a flaxen sorrel. The horse on the right
Is a liver chestnut.
Love That Chapelle, owned by MJ Farms of Veguita, New Mexico, is a sorrel.
Big Daddys Caddy is owned by Robert and Sandra Ogden of Shadow
Hills, California. The mare is a sorrel with a sooty flaxen mane and tail.
PHOTO COURTESY OF OWNER
This youngster is a liver chestnut with a flaxen mane and tail.