Here i come to answer your question.

Whats the Difference between a Stabilator and a Stabilizer?

Well a Stabilator is an all moving tail unit (usually the Horizontal Stabilizers) that moves the entire unit and there for pitches the plane up/down, this is most commonly seen in fighter jets because it enhances maneuverablity compared to a regular stabilizer. Where as a Stabilizer is fixed and has a control surface doing the pitching, and there for its less maneuverable but decreases the risk of stalling.