Medical oxy is very pure, while welding oxy can contain significant amount of just about anything. A flame isn't as particular about what it's being fed with as a pair of lungs are.
There is no difference in the gas, they both come out of the same tap. Gas suppliers are too cheap to have 2 separate containers for Oxygen so everything they sell is USP( that means it is safe for consumption). They 1 difference is a welding tank is not evacuated between refills and a medical tank is.