Cognitive-behavioral therapy is a theoretical therapeutic school in which the main focus are your behaviors and your conscious thoughts that you can report. It differs from psychodynamic therapy in that you are the expert on your own thoughts, and the therapist works with what you can report (as opposed to interpreting dreams, etc.). As it has evolved, CBT has increasingly involved emotional regulation. Dialectical behavior therapy, a "third wave" type of CBT (with behaviorism being the first wave, cognitive-behaviorism being the second wave) that was designed to help people with personality disorders regulate their emotions (and by extension, their cognitions and behaviors). DBT was originally tested on borderline personality disorder, and it has been extended usefully to other problems as well.
Schema therapy is a type of cognitive-behavioral therapy. Schemas are basically complex templates that we get from our past experiences that we use to understand our current situations, to predict what is going to happen next in any given situation, and to guide our behaviors. People with personality disorders typically have unbalanced schemas that lead to distorted expectations of what is going to happen next, very rigid predictions about others and the future, and sets of behaviors that interfere with relationships and good life functioning. In fact, the whole idea of a personality disorder is when a person's schemas are distorted and don't work well to guide the person through their life, and therefore they get stuck in rigid patterns of behavior rather than being able to flexibly adapt to situations. It's another way of looking at the idea of a "self-fulfilling prophecy." People expect certain things out of life, and inadvertently behave so as to get those things. Those things can be rejection, lack of understanding from others, failure, etc. Schema therapy works to help balance out those schemas and to test new kinds of behaving. New kinds of behaving can lead to new insights about what works and what doesn't, which hopefully leads to more flexible behavior and then to new kinds of thinking and ultimately to new and better feelings.
As psychology and the process of psychotherapy grows and evolves, though, the different approaches increasingly borrow from one another. Not all types of therapy are the same, just like not all therapists are the same, but as the discipline matures, the different ways of doing therapy are crossing over. So, even though CBT started out only dealing with what can be observed or reported, it is increasingly evolving new ways of getting to those hard-to-reach areas of human experience.
Hope this helps.
