There is no difference between Zhu and cinnabar. Cinnabar plays the role of exorcism. It is usually used in folk activities, just to show good luck. Cinnabar is red and festive.
There is no essential difference between cinnabar and Cinnabar, but their names are different. Cinnabar is called "Cinnabar" in ancient books and listed as the top grade. Dan is cinnabar, so it is called cinnabar. It was once produced in Chenzhou, Hunan, so it is also called "cinnabar".