Confusion about "Rod of Asclepius" and "Caduceus"

I came across the following article on Wiki and finally learned the difference between the one-snake-rod-of-Asclepius and two-snake-caduceus, a common mistake.

http://en.wikipedia.org/wiki/Rod_of_Asclepius

The caduceus is the staff that Mercury holds, with two snakes and a pair of wings, while the rod of Asclepius symbolizes medicine, which derived from the legend that Asclepius learned medicine art from Chiron.

(btw, talking about Chiron, it is the superlative form of centaurs. It is nice and civilized, not like centaurs with all the drinking problems. The large vaccine and Diagnostic company Chiron, now part of Novartis, derived its name from the legend, too)

Lost of people misused the caduceus as the symbol of medicine, including quite some insurance companies, and Medical Department of US Army probably because the caduceus represented alchemy and Hermes in the Greek mythology...