Premonition Dreamss are dreams that reveal a future event to the dreamer(however, in The Lich (episode), Finn's dream apparently happened either in the past or actually while he was dreaming. Their contents vary widely, but each contains the Cosmic Owl. Croak dreams, a subset of premonition dreams, reveal how the dreamer will die.
In "The New Frontier," Jake has a croak dream about a Banana Man and a rocket ship in space, and suffocated because he did not have a space helmet. At the end of dream, the Cosmic Owl appears and wakes Jake up, which Jake claims confirms it was a croak dream. It is unknown whether one can cheat fate by avoiding a croak dream's circumstances, but Jake says it is impossible. It does seem possible, however, for one to indefinitely postpone one's fate, as Finn's presence postponed Jake's, since at the end of the episode, Jake states that the events in his dream will happen again when Finn is not around.
In "The Lich," Finn has a premonition dream. In it, the Cosmic Owl appears on a TV that Finn is watching. At the end, the Lich leaves the snail he was possessing and kills Billy. When Finn and Jake arrive at Billy's cave, Billy appears unharmed, but it later revealed that the events of the dream had already happened by then and that the Lich is wearing Billy's skin.
In "Frost & Fire," Finn learns of his future breakup with Flame Princess when the Cosmic Owl tells him he "blew it" in his dream. Jake calls it a "prophetic dream," though the two terms are likely interchangeable.
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