The two different versions of the game appear to take place in two different books, with two different characters as player avatars. According to Andriasang, "Kiina's" volume is about protecting a blue gem from "strange but cute" characters, while "Piina's" volume is about collecting red candy. Kiina's game is subtitled "puzzle" while Piina's game is subtitled "battle," suggesting more fundamental differences.
We'll find out soon enough, as both games will be available in Japan on June 8, and the Japanese teaser site displays an ESRB rating, indicating a North American release is also on the way.