A Full shot utilizes the full arc and power of the swing, maximizing the distance traveled. The ball travels most of its distance in the air. This is the shot you'll use most times.
A Punch shot is a lower trajectory shot, using about 3/4th's the backswing but still most of the power, creating a shot that rolls alot more after hitting the ground. Good for medium distance approach shots to level greens with lots of area to roll, and also for getting out of the rough and certain sand situations.
A Pitch shot uses about 1/2 the backswing and will act alot like a Punch shot, but the distance traveled will be less, as less power is transferred to the ball. Good for shots around the green that are too far away to chip.
A Chip shot uses about 1/4 the backswing and is more of a gentle shot than a Pitch. The ball travels about 2/3rds of its distance in the air, and rolls the rest of the way. Used when you are just off the edge of the green or on the fringe and don't want to putt.
A Flop shot is a specialty shot which utilizes the full backswing and power of a wedge, but the clubface is wide open, resulting in a shot that pops up high into the air, but travels about 1/3rd the distance of a Full shot. There will be very little roll after landing. Good for areas around the green where you need the ball to travel over something, like a bunker, to get to the hole.