Massage training and licensure is regulated differently all over the world, and all over the United States. In the U.S. massage therapy is regulated on a state-by-state basis. State law regulates the practice of massage and different states have different (or no) regulations and names. Some countries are regulated on a national level. Some are not.
Below you will find a listing of some of the different designations. In order to understand what each desgination means you will have to search the regulations in the state through which the therapist in question is licensed/registered/certified/regulated. In some states massage therapy is managed by a body that regulates nurses. In others, a chiropractic or other allied medical health professional organization regulates massage therapy. Still others are regulated by stand-alone organizations dedicated only to massage therapy.
It is also important to note that many therapists practicing in America choose to become "nationally certified" by the National Certification Board for Massage Therapy and Bodywork (NCBTMB). In some states, this certification is required for licensure/registration/certification, but it is not typically enough to allow a therapist to legally practice in a regulated state.
CLMP - Certified Licensed Massage Practitioner
CLMT - Certified Licensed Massage Therapist
CMP - Certified Massage Practitioner
CMT - Certified Massage Therapist
LMBT - Licensed Massage and Bodywork Therapist
LMP - Licensed Massage Practitioner
LMT - Licensed Massage Therapist
MLD - Manual Lymphatic Drainage Therapist
MT - Massage Therapist
NCTMB - Nationally Certified in Therapeutic Massage and Bodywork
NCTM - Nationally Certified in Therapeutic Massage
RMT - Registered Massage Therapist