From what I understand, Li Zhu used the last of his soul to force himself to be reincarnated. When he was reborn, he was basically an empty shell. That's why as a baby and a toddler, he was mute and sickly. The fairy recast a soul in the body. Basically, put a new soul in the body. So it is a reincarnated body (that's why he has his powers and affection. So more like muscle memory) but it's a different soul. He really is not Li Zhu.