Z. Jujuba is the more common jujube you find in California. There's been breeding work done here in California and extensively in China. The fruits are much more sweeter and more airy & drier compare to Mauritiana. They are eaten both fresh and dried. These are the fruits you typical see dried called Chinese dates and used in traditional Chinese cooking. The fruits dry really well on a tree. The trees goes dormant in winter. They are more suited for dryer climates.
Z. Mauritiana is usually called Indian, Thai, or Taiwan jujube. Most of the breeding for them has been done in those areas. They are more suited for tropical or at least subtropical climates. For fruit sizes, some are the size of jujuba or smaller but some varieties are the size of small apples. The larger varieties are bigger than jujuba. The fruits are much milder in sweetness and much more juicier. They are for fresh eating. They do not dry well like jujuba. In my zone, 10 CA they don't go dormant but will stop growing in winter. In colder areas it may drop their leaves but I'm not sure if it's a true dormancy like jujuba. Once establish both grow aggressively but Mauritiana seems to be the more aggressive grower here since they don't go dormant and has a longer growing season. I do not know how it will do in frost. Both species can be aggressively prune back and still produce fruits.
I've heard they are not graft compatible. But not sure if that's due to rootstock going dormant. There's been other deciduous trees with non deciduous relatives like the persimmon and black sapote that were successfully grafted. But I don't know how long those experiments lasted and if there was any graft compatible issues in the future.