The difference is what causes the "Fault". Most faults, such as the many around the "Ring of Fire", occur on the edges o continents and ocean basins. Thus the "Ring of Fire" is the land masses of Asia, American, Antarctica, and Indonesia come into contact with the Pacific Ocean and are slowing making that Ocean smaller. The Africa Rift valley is a similar fault but between the Africa Continent and a new split from what is now Saudi Arabia (The Dead Sea is part of this Fault, as is the upper reaches of the Nile). There is a similar conflict between the African Continent and the European Continent (Leading to the alps, as Africa pushes under Europe as Africa heads north).
The Caribbean Islands are similar, caused by the Southern American Land Mass pushing against the North American Land Mass. This produces a fault, but since both Land Masses are heading Westward more then to each other is is small compared to the "Ring of Fire".
Ne Madrid is different, it is in the middle of a Continent not on the edge of the Continent. How they form, why they form AND what triggers them are not as while understood as when two land masses come into conflict. New Madrid is NOT a "Hot Spot" such as Hawaii or Yellowstone ("Hot Spots" are relatively fixed and the land masses float over them, thus island, like Hawaii build up as the Ocean goes over the spot, but as that spot moves away from the Hot Spot, buildup ends and the island starts to decline (and a new island developers where the land mass has moved over the hot spot). Thus the Hawaii Islands each started as a island build up by the Hot Spot, then slowly grew smaller as that island cease to be over the hot spot and a new island gets built up. Right now the Big Island of Hawaii is over the "Hot Spot" but there are indications that the Pacific Ocean has moved enough for another part of the Pacific is over the "Hot Spot" and will slowly start to build up a new Island as volcanic activity on the Big Island declines (The decline has not yet been detected to the best of my knowledge and the "new island" is just a small variation of the Lava going to the Main Island, but the start of the Change has began). Yellowstone is another "Hot Spot" and the North American Continent movement over that "Hot Spot" has been traced almost all the way back to where California first went over that "Hot Spot". I point out these two "Hot Spots" to show that New Madrid is something different. While New Madrid is different it also does not seem to be in contact (i.e. affect or be affected by) with the Faults of the Caribbean
New Madrid Fault:
http://en.wikipedia.org/wiki/New_Madrid_Seismic_Zone#2009_Research_indicating_the_fault_may_be_shutting_downhttp://www.whoi.edu/oceanus/viewArticle.do?id=3964On the Caribbean fault:
http://www.newscientist.com/article/dn18398-caribbean-at-risk-of-more-large-earthquakes.html?DCMP=OTC-rss&nsref=environmenthttp://en.wikipedia.org/wiki/Caribbean_PlateMap of the Plates and faults in the Caribbean:
http://en.wikipedia.org/wiki/Caribbean_PlateThe two biggest tectonic plats are the North American and South American Plates, but between them you have the North Andes (Columbia North of the Andes Mountains), Panama (Mostly the isthmus itself and Costa Rica), the Caribbean Plate, Central America excluding most of Guatemala, Panama and Costa Rica and most of the Islands of the Caribbean excluding Cuba (Cuba is in the North American Plate and the the fault separating the two plates is between Haiti and Cuba).
to see a map of the World Plates and a detail report on the Caribbean Plate go to:
quake.usgs.gov/~waltermooney/Caribbean2.ppt