I think the therapeutic approach is often independent of whether the degree is in clinical or counseling psychology. Different therapeutic approaches could be CBT, psychodynamic, humanistic, eclectic, etc. There are also specific therapeutic techniques to use with trauma, and which ones the T uses can also be independent of the degree, therapeutic approach, etc.

One of my therapist's specialties is trauma. His therapeutic approach is humanistic/eclectic/family systems. His degree is a master's in psychology. Some of the techniques he uses with trauma include talk therapy, EMDR, and psychodrama. There are others too. He weaves them together, depending on what is the best fit for the individual client.

I think a good start in finding someone to work on trauma with you is to ask them if they are a trauma specialist.