In Chapter Seven we learn that the Bennets' coach horses "are wanted on the farm," and therefore Jane "was obliged to go on horseback" to visit Netherfield.
I assume therefore that coach horses were a different category than riding horses.
There is perhaps another stratification: the landowner whose horses perform multiple tasks (working both as draft horses on the farm and drawing the coach), versus a wealthy landowner such as Darcy, who presumably has horses dedicated to transportation.