Like Chiilaa and Drafty said, genetically, as far as base
coat goes, there is no difference between this
as both of those horses are genetically e/e (red)
However, whether you use both terms to differentiate shade will greatly depend on where you're from and what circles you run in.
Where I'm from, there are 3 recognized shades that have their own names...a sorrel
, like the first one I posted and any other red horse that leans toward an orangey color; a chestnut
, which is a deeper, richer red like this
And a liver
chestnut, like the other one I posted above.
BUT, there is absolutely nothing wrong with calling all "red" horses either sorrel or chestnut as both are technically correct...though chestnut is more widely recognized.