This article is from the Medical Education FAQ, by eric@wilkinson.com (Eric P. Wilkinson, M.D.)with numerous contributions by others.
Before discussing this, it may be useful to delineate the
differences between organizations that physicians may be associated
with. Some definitions:
Association or Academy - A group for physicians in a particular
field, that often sponsors meetings and publishes journals.
Example: American Academy of Family Physicians.
Board - Organization that conducts periodic examinations for
physicians in a particular field, and offers "certification" (cf
7.8). The overseeing organization for all specialty boards is the
American Board of Medical Specialties <http://www.abms.org>.
Example: American Board of Internal Medicine.
College - Similar to an association, but membership is often tied to
board certification and experience. More of an honor than simple
association membership, doctors are often elected to "fellowship"
after recommendation by their colleagues. Example: American College
of Surgeons.
After a physician has received board certification in his/her field,
and has gained a set amount of experience in that field (usually a
specified number of years of practice), that physician can be
recommended for fellowship status in their specialty college. After
approval, the physician can then use their fellowship status on
stationery and business cards, i.e. Susan M. Avery, M.D.,
F.A.C.S. signifies that Dr. Avery has received fellowship status in
the American College of Surgeons.
 
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