The snatch pull to the knee is an exercise that helps improve the strength of the muscles involved in pulling the barbell off the floor during the snatch.
The snatch deadlift from blocks above the knee is used to create neuromuscular facilitation for subsequent snatch training, as well as helping to strengthen the torso.
The press from split position is an exercise to help strengthen the athlete's position in the split of the jerk, as well as improve the balance in that position.