I’ve been wondering this, and so far nobody has given me an answer for it.
Why is it that some Caduceus have two snakes and some only have one snake? A
good example of this is a National Registered E.M.T. and a Navy Corpsman.
The symbol with one serpent is the Staff of Aesculapius. Aesculapius was the god (or demigod) of medicine.
The symbol with two serpents is the Caduceus. It was a symbol of Hermes or Mercury, a god of trickery, thieves, and lawyers (and also the messenger of the gods). It is used a symbol of messengers and diplomats.
Obviously there is some confusion between the two symbols. There may even have been confusion among the ancients. The caduceus seems to be more commonly used by the medical profession in the U.S. (it is the symbol of the medical branch of the U.S. Army, for instance). But the Staff of Aesculapius is commonly used in other countries. I believe the Staff of Aesculapius is becoming more common in the U.S. in recent decades.