The caduceus (☤) is the traditional symbol of Hermes and features two snakes winding around an often winged staff. It is often mistakenly used as a symbol of medicine instead of the Rod of Asclepius, especially in the United States. The two-snake caduceus design has ancient and consistent associations with trade, eloquence, negotiation, alchemy, wisdom, and controversially, thievery, lying, and the passage into the underworld.

The modern use of the caduceus as a symbol of medicine became established in the United States in the late 19th and early 20th century as a result of documented mistakes, misunderstandings and confusion.

The good news is that both have their own unicode symbols, ⚕ and ☤.

source: grugq