Papers like the Canson Rag Photographique and Epson Legacy Fibre are both smooth matte cotton papers with no OBA, and a high level of whiteness. Canson lists the CIE whiteness of both the Rag photographique 310gsm and Platine Fibre Rag at about 89. Whitening agents in semigloss papers (or coatings) can include stuff like Barium Sulfate (baryta), titanium dioxide and white silica. However, I'm not sure (and companies are unlikely to share) what is put into the OBA-free matte cotton papers that helps get them so white.
I wouldn't be surprised, based on the description, if the "bright white" paper is similar to the Legacy fibre, while the "polished rag" is similar to a platine-type paper.
Mike