How could banlists be so radically different?
Well, TCG (Trading Card Game) and OCG (Original Card Game) are two separate and different games actually; you can't use cards from one on official games from the other. I am not Konami, but seems logical to me that such lists exist separately.
As you probably know, Yu-Gi-Oh! started first as a Manga, and then an Anime went out (and then translations). Only after some time later is that the OCG was created, and shortly after the TCG. We can see that since it's inception they were conceived differently and for different target audiences.
Another reason that justifies different lists is the fact that cards first come out on OCG, and some time later they appear (or not) on TCG in the latest Booster set available.
This means that for a period of time some cards actually don't exist on the TCG and are legally unable to be played on official events. This shows that OCG has different needs/situations, and at different moments, than TCG regarding the cards that need buffing, nerfing, or erratas.