Left-Footed Kickers, Right-Footed Kickers, and Switch Kickers
Switch kickers are players who can kick on either side of the plate. They usually are not ambidextrous themselves, they have just been trained to kick both left-footed and right-footed. Being a switch kicker is useful because they can kick a pitch in any direction.
Square Stance, Open Stance, and Closed Stance
A square stance is the most common stance. The kicker stands with both his feet an equal distance from the plate, and parallel to the side of the kicker's box. It allows kickers to see the pitcher with both eyes, and to be in a good, balanced position to kick any pitch.
An open stance is when the kicker stands with his front foot farther from home plate than his back foot. This causes his chest to be facing the pitcher slightly, making him open to the pitcher. It allows kickers to track the pitch better, and to pull the kickball.
A closed batting stance is when the kicker stands with his back foot farther home plate than his front foot. Since this causes his back to be facing the pitcher slightly, he is closed to the pitcher. Although this stance makes it harder to see the kickball, some kickers claim it helps them hit the kickball more powerfully.