Actually........
The difference is not just paperwork but in the way the cylinder is prepared. All O2 does indeed come out of the same "tap" at the depot but is the cylinder handling that differentiates what goes on the paperwork. Weldon O2 the the cylinder is just filled and sent out. Any gas designated as a breathing gas has the cylinder vacuumed and then the contents are tested to ensure they meet a minimum purity rating.
Water content is a misnomer as all O2 is actually produced the same way these days, false economy to do otherwise.
The minor problem with using welding O2 is that you could get contaminated gas. The chances are incredibly small and actually only matter when going down not up. We breathe so many impurities daily it makes little difference (smokers intentionally breathe in CO!).
Using contaminated gas for diving is where it gets really dangerous. I will save the theory on gas exchange for another day.
Personally for anyone wanting to fill there own ask for diving O2, it makes about £3 difference for a J cylinder and is certified as a breathing gas.