How do stabilizing and disruptive selection differ? ?

Both are types of natural selection observed by ecologists. 
Stabilizing selection is the most common type, and acts as a natural filter for extreme values, while favoring averages. A good example would be baby size, as a too small baby would be weak and too exposed to illnesses and a too big baby would increase the chance of killing the mother while passing through the pelvic canal, thus increasing its chance to die.
Disruptive selection is the opposite: averages being not as fit as extremes for certain tasks, they disappear from a population. For instance, some animals have two male mating strategies that work well with females: either the male is the biggest possible, and protects a territory with females to mate with (alpha male), or the male can also be very small and yet maintain its ability to mate with females (drone males). Those drone males may look like females to other bigger males and can then mate with females protected by the alpha male. An average male wouldn't be able to fight off an alpha male, and wouldn't be able to look like a female, so wouldn't reproduce as much.