As a psychologist that treats sexual disorders, I believe that most of the people involved in medical play do not have Munchausen's but simply have fetishes or associated paraphilias.
Flyfisher makes a few important distinctions about some differences of mental disorders, but not quite specific enough. Here are a few definitions, taken directly from the American Psychiatric Association's Diagnostic and Statistical Manual of Mental Disorders, Fourth Revision(otherwise known as DSM-IV) This is the bible of Psychiatry:
Factitious Disorder: is characterized by a person intentionally fabricating or inducing signs or symptoms of other illnesses solely to become identified as "ill" or as a patient (also known as Munchausen's Disorder). This is not limited to a person feigning symptoms but actually committing acts that would induce sickness (I have had many patients that do this for attention such as one who drank bleach to induce vomiting and create digestive problems warranting hospitalization. (See Munchausen by Proxy)
Munchausen by Proxy: this is a person committing acts to make another person ill for the purpose of a)gaining outside medical attention for that person, and b) taking on the role of caregiver to appear favorably to outsiders (eg: mother in Ohio who shaved her son's head regularly and fed him arsenic to make him sick and told him and others that he was dying from cancer.)
Somatization Disorder: Physical complaints that, after significant examination and testing, cannot be fully explained by any known general medical condition or the direct effects of a substance.
Malingering:the intentional production of false or grossly exaggerated physical or psychological symptoms motivated by external incentives" (American Psychiatric Association 2000). External incentives that may motivate a person to malinger symptoms include avoiding work, evading criminal prosecution, obtaining drugs, receiving financial compensation, avoiding military duty, or escaping other intolerable situations. Some of the most frequent complaints include gastrointestinal problems (mostly in women and children) and back pain as both are attributable to many conditions that are very difficult to diagnose.
Side Note: While the above diagnoses are valid, the criteria mentioned above are alone not sufficient to make a diagnosis of a person with these symptoms, as there many other criteria that need to accompany for the diagnosis.