I don't understand your question, Taiyo Yuden discs don't come under their own "Taiyo Yuden" brand, this doesn't exist. "Branded" Taiyo Yuden is third-party branded, by Verbatim, Plextor, TDK, Fuji...
The only exception is in some countries (mainly Japan), where Taiyo Yuden has its own brand, which is "That's".
All online stores advertising the "Taiyo Yuden brand" are referring to unbranded Taiyo Yuden discs. I understand you confusion. :doh:
I think that in the USA, the unbranded are cheaper than the third-party branded discs, so people buy more unbraned but in Europe it's the other way round, so personally I only buy Plextor-branded or Verbatim-branded TY discs. - this does not mean that the unbranded are less good, not at all :disagree: