Even if there were only two manufacturers the oxides could be different between SS and WSP. Also, perhaps similar oxides produce similar colors without being the exact same chemical formulation.
Take TiO2 for example. It's titanium dioxide, the same everywhere. But there is oil soluble and water soluble. That doesn't come from the TiO2. It must be something mixed with the TiO2 that determines water or oil solubility. I imagine it's some carrier powder...
I expect the answer to my question is that oxides are indeed the same everywhere, but I'm asking because I'm not sure.