White Zetsu and Black Zetsu have no special relationship.
The two were named after Ban, because Bai Zetsu's shape is very similar to Black Zetsu and is white, so they were named Bai Zetsu.
Black Zetsu is Kaguya's child. From birth to now, his purpose is to resurrect his mother. He first divided the descendants of the Six Paths Sage into the Senju clan and the Uchiha clan. In order to break the seal , several types of chakra must be activated in the Infinite Tsukuyomi, and the tailed beasts must also be collected. The premise is that this person must have the Samsara Eye. In the process of searching for the Samsara Eye, Black Zetsu went through thousands of years, and finally he believed Madara It was bound to succeed, so the plan began to be implemented. Black Zetsu disguised himself as Madara's product, allowing Madara to prompt Obito to establish the Akatsuki organization, and then collected the tailed beasts. Madara launched the Eye of the Moon plan. Black Zetsu took advantage of the situation at the end and attacked Madara unprepared. The chakra was concentrated on Madara. In his body, Kaguya was successfully resurrected.
Bai Zetsu was a person from Kaguya's period at the beginning. Kaguya launched the Infinite Tsukuyomi and controlled everyone on the earth in illusion. After thousands of years of changes, Bai Zetsu's character was formed. look.