The symbol on the left is the caduceus or a herald's staff. In Greek mythology, it is an attribute of Hermes, the god of messengers, economists, merchants and - incidentally - gamblers, liars and thieves. Hermes is the closest Olympian god to economics and business, that's why the caduceus shows up on this website - and in the seal of some economics schools, for example this one or this (more stylized) one.

How the caduceus ended up as a symbol for medical institutions in the U.S., I don't know. Maybe it got confused with the Rod of Asclepios?