The three "big" medical student organizations are AMSA, AMA-MSS, and the OSR (the organization of student representatives, which is part of the AAMC).
AMSA has the reputation of being the most "radical" or revolutionary, as pointed out by the nay-sayers on this and other threads. And, they certainly are political beyond the scope of issues that directly affect medical students. (I didn't read the link about their history but my understanding was that they broke away from the AMA because it was too conservative).
Here's the history of the AMA-MSS and AMSA together:
http://www.ama-assn.org/ama/pub/category/8799.html
Anyway, it looks like the AMA, in an effort to more directly deal with the issues of medical students, eventually blossomed into the AMA-Medical Student Section. However, again - the focus of the organization is the medical profession and its place in this country, and this is just the student section of that organization.
The OSR, however, is specifically targeting medical education. All AAMC accredited schools are members of the AAMC. As part of that institutional membership, schools are allowed to have 4 student representatives to the OSR. These reps go to national and regional meetings to discuss issues facing medical students directly. There are five broad areas that they focus (medical education, legislative affairs, student well-being, community & diversity, and communications). The OSR also has liaison positions to most of the aspects of the AAMC that affect our lives (MCAT, admissions, ERAS, NRMP, USMLE, LCME, etc etc). However, the OSR has the reputation of being "slower" to respond to change, since it's a consensus driven organization and also part of the larger AAMC. Plus, schools have different levels of involvement (many students are unaware of this organization, whereas other schools incorporate the OSR positions as a key part of their student government and campus presence).
