Playing with semantics is for lawyers, not for life. "Shoot to Kill" does in no way imply that you are going to shoot until the person is dead. No one here is advocating execution.
Shoot to Kill, in my mind, and I'm sure the minds of the others who have voted this way, means AIM to Kill. And don't play semantics with aim as in "My goal is to kill."
It means when the threat appears, I will make no false pretense about what is going to happen. I am going to shoot the person who is threatening my life and/or the lives of others and I am going to aim for the vitals.
If anything "Shoot to stop" implies some sort of escalation later that seems dangerous to play with. If someone assaults you and/or your family with the intent to hurt or kill you and lets say some grand deity comes down and grants you 100% shot accuracy in one of two areas. Area 1: The Hip. Area 2: The Forehead.
What shot do you take? You take the forehead, unless you're hoping to take a few rounds yourself.
You need to fully realize that pulling the trigger is a death sentence. Assume that every bullet is a life ender. Make no bones about your resolution. You're either willing to kill this guy or you're not. For your sake and your families, don't pretend there is some escalation ladder where you have to follow a long list of checkpoints before aiming at someones vitals.
You react. If you issue a command to stop, or draw your gun, and the intruder does not stop, the next stop is shooting the vitals. Period.
Or, for example, think about the recent church and mall shootings. Do you take a checklist approach to someone in the middle of the massacre or do you take an open opportunity to kill the murderer before he continues? Call me crazy or whatever you want, but I'm not risking my life or the lives of more people by taking a shot that won't result in him going down. If I hit him and he goes down and is still alive and screams I give up, fantastic. He'll go to trial. If I hit him and he dies, the threat is over and lives have been spared.
The semantics have been played with far too much in this thread with one side assuming shoot to kill means "Execute the person no matter what" and "Shoot to Stop" involving some sort of escalation ladder, which is something I pray you aren't considering.