You are correct the O2 is O2 regardless but the quality of it may vary.. this is from AOPA...
All oxygen supplies come from a very small number of vendors and is normally delivered in 25,000 gallon refrigerated tanks. The manufacturing process is so thorough and clean that the finished product meets all usage specifications right from the tank. However, just to be sure, any lot of oxygen destined to be medical oxygen is batch tested for aromatics (oils, Benzene, and other impurities that appear in the manufacturing equipment). ABO (aviation breathing oxygen) is also tested for moisture content, while welding oxygen comes straight from the vendor with no additional additives or testing.
FAR Part 135 requires that the operator must provide ABO or an “acceptable replacement.” But under Part 91, it is at the pilot (operator’s) discretion. Although hundreds of FBOs around the country have aviation oxygen available, industrial oxygen (remember, it’s all the same) can also be used for Part 91 operations.