The color names chestnut and sorrel are used in different ways by different groups. They are genetically the same base color, red.  Many experts call a horse with red pigment only a chestnut.  If that horse then is lighter at the bottoms of the legs, around the mouth, and at the "armpits" (what come call "pangare", or "mealy"), then they call it a sorrel.

Amir Halam, an Arabian, is registered as a "chestnut", though his lighter lower legs, clearly seen if you click this picture, are characteristic of a "sorrel".
The Irish Empress by The Scarlet Irishman and her filly by Mr JB Dude.  Sorrels owned by Barbara Burton; This photo is actual size.	Brians Texas Star submitted by Pamela House Sire: Bay. Dam: Bay Photo no longer available, sorry.  We'll try to get it again.
This colt looks "sorrel" in these early pics ... but it's just "foal leg color"!  See him older at the right. Click these 2 pics for larger ones.	Skip The Holidays "Skippy"  ...as he aged, he became a solid rich brown color all over, making him a "liver chestnut".  Owned by Susan Prouty, Tanglewood Farms ...by Holidays Kricket and out of San Star Heidi. This photo is actual size.
Wimpyschoclatshodown, Dark liver chestnut. He is the IQPA representative. This photo is actual size. Submitted by:  LaDonna Foster, International Quarter Pony Assoc.

How cream genes affect a red (chestnut/sorrel) horse:

red + one cream gene = Palomino

red + two cream genes = cremello

See the color chart or interactive page for illustrations.