Like said, sorrel and chestnut are genetically the exact same. Sorrel is a term only accepted by the APHA and AQHA and is used in the western world, usually referring to the light almost orange colour that chestnuts can get. Any other breed is a chestnut, regardless of shade.
Actually, equiniphile, flaxen is a gene that only affects sorrels/chestnuts and that's why their manes and tales are lighter like that and it should be used when describing the horse. Kind of like referring to a silver bay, you wouldn't just call it a bay. I would say your guy is a flaxen chestnut. He has a lightened mane and tail, a lightened muzzle, and some lightening on his legs. My friend's flaxen chestnut TB has the same colouring.