The main difference is that the person with Munchausen syndrome seeks medical attention to deal with severe emotional and mental problems, while the person with hypochondria (health anxiety or illness anxiety disorder) seeks medical help as they have the belief that they have a serious medical illness. So a person with hypochondria actually believes they have a medical illness, while one afflicted with Munchausen syndrome has such low self-esteem and identity issues that they would fake physical symptoms in order to get medical attention, and this is an attempt to deal with this emotional problem.
Hypochondria has a better prognosis, as the treatments for it are similar as for anxiety disorders. The following video explains how hypochondria can develop, and how it can be treated:
On the other hand, Munchausen syndrome is a severe emotional and mental problem, and requires the expertise of a multidisciplinary team. The focus of such team involves communicating with each other to provide desperately needed mental health treatment, rather than more medical procedures and medical tests.