Fozzy,
MAPS-Maitland, IAOM-Texas Tech, NAIOMT, among others use the "COMT" designation. Other manual therapy certifications you may encounter include MCMT from Hands-On Seminars, cert. SMT from Spinal Manipulation Institute, MTC from St. Augustine, among others I'm sure.
Within NAIOMT, the "CMPT" designation means you have successfully passed oral, written, and practical tests through their Level 3 coursework while "COMT" means you have successfully passed Level 3 and Level 4 coursework.
As to why one may choose one over another varies. Cost, influence from mentors, influence or affiliation with the entry-level institution one went to, location of offered courses, plus many more could be factors.