A sprayed in liner is just that, a spayed on bed liner.
A bed mat is just like you assumed, something like a 3/8" Dee Zee rubber mat that prevents the camper from sliding.
A horse stall mat is much heavier and thicker than a regular bed mat. Some folks use these to raise their camper higher to clear the truck bed rails or other obstruction in the bed.
I use a rubber bed mat on top of the sprayed in bed liner to keep my camper from shifting and also to protect the camper bottom from the irregular shape of the truck bed floor (ridges and valleys).