There are three main differences between each type of quest which includes Xuanhuan quests, Kongming quests, and Zhuanxu quests. The first one, Xuanhuan quests, have a few differences from the original story. There are main characters in this mode which may give you a different story kind of feeling when reading it.
The second one mainly focuses on the origins and mysteries of certain things around Konoha. The last one is based upon stories from Zuixian Pushe, there are quite a lot of non-canon naruto elements in this mode as well as funny changes made by Inoichi Yamanaka's spirit clones.
In addition to that, each type has its own exclusive cards and titles related to them with Xuanhuan cards being ranked SSS grade and Zhuanxu being SS ranked only.