Which came first Rave Master or Fairy Tail?

I noticed that Plue, the little snowman dog thing, is in Fairy Tail, a manga by Hiro Mishima. In Rave Master, also by Hiro Mishima, Plue is the main characters little friend that goes with him everywhere. Is it the same Plue? I also noticed that the Lightning guy from Rave master is alson in Fairy Tail. Is he the same guy? Is Fairy Tail supposed to be intertwined with Rave Master? Which is supposed to come First?