In a lock out punch, the arm is thrust out to about 98% of the elbow's extension, and then the arm is held in an isometric contraction, motionless, for a second. In a snap back punch, the arm is thrust out in the same manner but it is quickly withdrawn without any apparent stoppage. Both punches impact the target using muscle power with the mass of the body behind them, the difference comes after contact is made.
In the lock out punch, the muscles contracting to thrust the fist into the target are contracted isometrically to firmly connect the arm to the torso, while protecting the elbow joint from injury due to high speed hyperextension. Contact time is extended. In the snap back punch, contact time is extremely short. Both types are appropriate for different circumstances, targets, and desired outcomes.
The lock out punch is useful for beginners to learn punching motions. Most patterns and one-steps use the lock out punch. For sparring, the snap back punch is usually more effective. Georges Carpentier, in his book The Art of Boxing says that a punch should move similar to a whip; it should quickly lash outward, strike your opponent, and be back to guard before the opponent knows what hit him.
If your opponent is charging forward about to run over you, then drive a lock out punch into them, with a firm connection to the floor to take the impact of impaling him/her. To drive an opponent backward, bury a lock out punch into them with deep penetration. To hit an opponent who is moving backward, use the snap back punch.
Locking out a punch leaves you vulnerable for a relatively long time. If you are dealing with a person who knows joint locks or wrestling technique, always snap back. During competition locking out punch wastes too much time, you need to snap back and quickly attack again and again until "Break!" is called.