Brian explained this very well to me in lesson we had.If you had a wheel with spokes,like a big bike tire and it was in facing you.Now you need to spin the wheel so the wheel would spin clockwise you would either grab the rim and spin the tire [pitch elbow] elbow leads the hand or you would grab the spokes and spin the wheel [punch elbow] hand leads the elbow.Another visual is a pitch elbow is like a karate chop the elbow leads the hand.A punch elbow is like if you were to hit a punching bag with the base of the palm of your hand.The hand would lead the elbow.
Pitch Elbow - Elbow, Hands, Clubhead
Easier to learn if you are a new golfer. Is often the only way a young golfer can swing. Pure pulling.
Punch Elbow - Hands, Elbow, Clubhead
Most golfers do this. Easier to do for more experienced golfers. Better for pushing, but you can pull too.
Push Elbow - Hands, Clubhead, Elbow
A great way to putt.