Puzzle & Dragons for smartphones doesn’t have a story. You’re just thrown into dungeons with a handful of monsters you can control by matching colored drops. In contrast, Puzzle & Dragons Z is a full blown RPG. Sure, it uses the same battle system, but GungHo Online Entertainment the parent company of Lunar developer Game Arts and Grasshopper Manufacture made a plot for the Nintendo 3DS game.
The story which is briefly touched upon in this video is about world where dragons and people co-exist thorough spirit power called drops. You play as a Dragon Tamer out to stop the Paradox Organization an evil group that wants to make paradise in this world crumble. Puzzle & Dragons Z will come out this winter for Nintendo 3DS.