Why might a large predator and a small animal that it eats have different adaptations?

Here is one reason:

A large predator may have little to no predators.  The small animal (which is eaten by the particular large predator may have different adaptations.  For instance, the small animal is at risk for being eaten by the large predator—and potentially other predators, too.  Some strategies might include mimicry, playing dead, camouflaging (e.g. blending in with blending in with vegetation),  producing in larger numbers (for survival of the organism—being "r-strategists".
   The large predator would tend to be a "k-strategies".  The large predator would not have to worry as much about be hunted for prey.  The large predator may have specific characteristics that differ from those of the small animal (which the said large predator eats) and many need different strategies (e.g. the large predator may be a reptile and need thermoregulation/ sensitive to temperature/ seasonal changes;  may change skin/coat color to absorb/reflect heat.

Not only is it the purchase of about 40% of america, it also grounds to on-go our advancement as a civilization.