Sorrel, chestnut, and liver chestnut are all the same color genetically, just different terms. You could call him chestnut or sorrel, whichever suits your fancy. Liver chestnut is generally darker.
As everyone said, they tend to be much darker. Just Google "liver chestnut" and click Images and the first half page of horses are all liver chestnut. When they're extremely dark with a pale mane and/or tail, they call it "burgandy chestnut" after a well know line of Arabians that display that color and the Arabian stallion Burgandy Sun. Posted via Mobile Device
He's a cutie, but just a regular chestnut/sorrel. Like everyone else said, liver chestnuts are much darker. Sometimes they are so dark they are almost impossible to distinguish from a black horse.
Pretty horse! He may very well shed out to be a liver chestnut in the Spring, my mare would shed out to be a liver chestnut in spring, but then got sun-faded, so was more of a normal chestnut.