They are actually the same thing... CBT is the name given to an overall therapy model, it is a quick name to say that you are entering a therapy that is both cognitively processing your memories within the correct areas of the brain, and also contains a behavioural component that is realistic for you to apply within your life, done via both exposure based and technique application within situations.
Cognitive processing therapy is just that, one part of a CBT model that is handling only the brain processing of the trauma. EMDR also does this, being it takes care of the actual processing of the trauma within the brain.
Cognitive processing is also a form of exposure, being that you expose yourself to the trauma again in order to process, based on failure to do so is fear based. So even talking about your trauma here, is both cognitive and exposure based, because your brain is processing what you did, and receiving feedback for you to process and apply to change your mental perception of your trauma. Pretty much everything we do in life is exposure therapy... being the act of doing. So the moment you think about something, you are doing. How far doing goes, changes the term exposure therapy into more depth from just normal exposure that is collectively referred to as cognitive processing.
Does that make sense?
In a nutshell, you need three things to make up the overall package, being:
- Cognitive processing with correct feedback loop,
- Actually removing fear based emotion through exposure exercises, and
- Stress reduction / management techniques and/or exercise/s.
All three are needed, which way you incorporate them, is unique.
Some might have EMDR + Prolonged Exposure Therapy + Weekly massage and learning stress management. Another could have, Cognitive Trauma Processing Therapy + PE + stress management techniques, relaxation, weekly golf, exercise, etc.
You get the idea no doubt. You can mix and match. Each complete package is called CBT, because it encompasses a cognitive processing, an exposure element and stress inoculation method/s to manage ongoing daily life.