Once upon a time, I worked for a paper manufacturer in the commodity paper side as a price analyst. One of our products we made was copy paper. And we often sold paper as brand name (Xerox, HP) and some as generic or private label (office depot). But they weren't necessarily the same paper. Xerox and HP (and companies like that) have very high quality standards. Not all of our machines could produce to that level all the time. Some older machines never could. But instead of letting the capacity sit idle, we still ran the machine and sold it as off-brand.
So, you see, just because the same company makes the 2 products (brand name and private lael) -- it doesn't mean that they are the same. Ingredients, quality control, manufacturing process can still vary. And often with private label, the company buys leftover capacity from SEVERAL companies.