What preposition is correct 'sleep on the bed' or 'sleep in the bed'

Are both expressions correct? If yes, do they have different meanings? It seems to me that I came across both of them in books, but I'm not sure.

Answer

They are both correct, but convey slightly different ideas.

I will sleep on a bed.

Implies that I will sleep on the piece of furniture I refer to as a bed. As opposed to sleeping on the couch or sleeping on the floor.

I will sleep in a bed

Specifically conveys the idea that I will be inside the bedclothes, typically underneath a blanket or duvet.