RN license means she has nursing background in physical health prblems like broken bones, and so on.

Certified clinical social worker means she is taking classes for the mental health field and is at intern level which is where she can see clients for mental health therapy but she has to meet her supervisor for "supervision" on all her cleints. She could also have completed her requirements for supervision and intern hours with clients but has not yet taken the state boards (exams) to recieve her state license for mental health therapist.

Clinical psychologist has already been through classes, internship, supervision and has their state license and most times has a specialized field that they work in (marriage and family, pediatric therapy, or specialized by disorder)

Neither one is allowed to dispense medication prescriptions.

And yes the new therapist will want your past therapists records. Though the actual files are not sent a photocopy of your complete file is sent to the new therapist.