In
Dragon Quest Monsters, you follow the adventures of Terry
as he's transported to the kingdom of Taiju to become a Master Monster
Trainer, win the Starry Night Tournament, and rescue his sister
Mileyu.
In
Dragon Quest Monsters 2, you take on the role of either Ruka
or Iru as they travel to the island of Marta to open a monster farm
with their parents. They'll have to train their monster team to
acquire magic keys that unlock portals to other worlds. There they'll
gather items to plug Marta's hole and stop it from sinking into
the sea.