There is a very important distinction between a plastic surgeon and a "cosmetic surgeon".
Plastic surgery is a medical specialty that is recognized by the American Board of Medical Specialties (www.abms.org), while "cosmetic surgery" is not. The ABMS is the only plastic surgery board recognized by the American Medical Association (www.abms.org).
A plastic surgeon has a complete residency in reconstructive and aesthetic technique at one of 89 plastic surgery programs in teaching hospitals across the country. There is no "cosmetic surgery" residency program recognized by the Accreditation Council for Graduate Medical Education (www.acgme.org). Be aware that anyone can call himself or herself a "cosmetic surgeon".
Why would someone operating on patients choose to be a "cosmetic surgeon" instead of getting the medical training necessary to be a board certified plastic surgeon? More than likely, they couldn't get in to the residency program or are too lazy to pass the rigorous testing involved. These are not traits most people seek in their surgeon.
Of course, "cosmetic surgeons" tend to charge less than plastic surgeons. Keep that in mind if you are price shopping for a surgeon.