DBT is a specific subset of CBT that deals with four parts: emotion regulation, distress tolerance, mindfulness, and interpersonal effectiveness. It was developed by Marsha Linehan in the 90s to treat BPD, but can be further extrapolated to other mental illnesses now. Really you focus largely on skills to get through difficult moments/situations in DBT. It’s pretty much all skill-oriented in my experience.

CBT is more broad. It works on the link between thoughts, feelings, and behaviors. In CBT you really focus on gaining control of your own behaviors and learning how to challenge certain unhealthy thoughts and manage your feelings.