The position on the left is a draw. "What?" I can hear you saying. Okay, I'll put it this way. White, in order to win, obviously needs to promote his Pawn. But the Pawn can't move at the moment, because the Black King is in the way. So White goes around the Pawn. 1. Kf5 Ke8 (the key move to draw as Black) 2.Kf6 Kf8 3. e7+ Ke8.
Okay, it's White's move. Of course, he won't move away from the Pawn, because Black would then snatch it up. But the only other move is Ke6. Stalemate! Black can't move next to his opponent's King, and d8 and f8 are covered by the Pawn!
If it were Black's move in the first position (above), he would move to e8, and the play would continue 2.Kf6 Kf8 3.e7+ Ke8, resulting in the same drawing position. The key to keep your opponent from queening his Pawn in this type of endgame is to keep your King in front.
This position is also a draw, much to White's dismay. It looks like White can win easily, but Black's King is in the corner where the Pawn needs to promote, and White's Bishop stands on the opposite color as the queening square. Pushing the Pawn at the moment just loses it, so White plays 1.Kg6. Stalemate again! If White plays his Bishop away to e4, then play continues 1...Kg8 2. Kg6 Kh8 3.h7 stalemate. However, White would win if his Bishop stood on a black square, because he could force the enemy King away from the corner.