A chip shot is used when your ball is off the green by only a few yards or less. The object is to keep the ball low to the ground while having the first bounce a few feet on to the green. The ball runs the rest of the way to the hole. The less green you have to work with, the higher loft you use. A higher loft club will run less.
A pitch shot is a shot designed to get the ball up in the air over a trap or when you don’t have a lot of green to work with (short-sided). It is used when you want the ball to stop quickly so it doesn’t run past the hole.
A punch shot can be two different things.
One with a short swing is just a longer distance chip. You are running the ball onto the green rather than having it land on the green and run to the hole. It is good to use when there is no hazard between you and the hole. In addition, firm ground and short grass is helpful so the ball doesn’t stop unexpectedly.
The other kind of punch shot is used to keep the ball low into the wind, to keep it under a low branch, etc. It is usually almost a full shot, but the position of the hands ahead of the ball at impact reduces clubhead speed so you use a little more club. It also keeps the ball from ballooning into the wind. It is a control shot that is closer to a full swing.
Using the correct shot can minimize the likelihood of a miss and maximize the likelihood of a good shot.