There is actually a difference between Chestnut and Sorrel.
Chestnut's have dark colouring in their mane & tails and are more a red/red or brown/red colour. A sorrel has flaxen mane & tail or light colouring mane & tail and copper/red or orange/red in body colour. I know this as I have a chestnut tb and a sorrel paint, they both look totally different. I think both the American and Australian Paint website's actually has pics of a chestnut and sorrel, and the paint society here in aus is now defining the difference.
Hope that helps
Happy Trails
Lea