The article CavSct posted is a pretty good explanation of the differences between the two. It's the same type of operation in terms of actually removing wood, the only thing that changes is the reference table. On the jointer, the face being cut is made flat with reference to the outfeed table it rests on after the cut (the plane of reference is the same as the cutting plane). With a planer, the face being cut is made parallel to the planer bed at a fixed distance. So the jointer doesn't give a rat's ass about the opposite face of the wood it is cutting, but the planer does. If you have two lumpy faces on opposite sides, the jointer will make one of those faces flat. The planer will spit out a lumpy board with the high spots no higher than a fixed distance from the opposite side.

If the board is reasonably flat to begin with, and the material is fairly short, the planer can flatten a board like a jointer if the differences between the high and low spots are within the capacity of the cut. However most of the time, if you put a warped board in the planer, what usually comes out the other end is a thinner warped board.