Not the same symbol.

The symbol with 1 snake around a stick corresponds to the earliest treatment known to mankind that was performed (and still is) in Africa.

There, they have a parasitic worm that burrow itself under the skin and just keeps growing near the surface. If they break, they give an incredibly burning sensation.

The treatment for these was to cut the skin just in front of one end of the worm then wrap the visible end of the worm to a stick and then turn the stick very slowly to extract the worm as it wraps around the stick. This was done to avoid breaking it in the process.

This is why you see the snake wrapped around the stick and, as the first known treatment, it represents health.

The one with 2 snakes is a completely different symbol with a completely different meaning, I'll let you explore that one.

Symbols are comprised of items that have relationships. missing a item *forces* these symbols to be different as it changes relationships hence symbolic