The use of deadly force in self defense is a shooting to kill.
Period. End of story.
Self Defense is a justification for what would be, in unjustified circumstances, murder.
You and everyone else may call it what they will to avoid looking directly at the cold hard truth: Putting the front sight on another human being and commencing a proper trigger press is shooting to kill.
Done with justification, it is self defense.
Done without justification, it is murder.
But it is still placing the front sight on target and commencing a proper trigger press.
The use of linguistic contortions is for people who are either not sure they can bring themselves to kill someone, or for people lacking a proper understanding of what self defense truly is, or those lacking the moral/ethical fortitude to look squarely at the results of a justified use of force deadly force...a dead person.
It's not pretty.
It's not politically correct.
When justifiable, it is not murder...and not subject to civil or criminal sanctions.
But it is still shooting to kill.
Calling it anything else diminishes the act, and that’s wrong.
Life isn't something inherently precious for everyone, because some people are cockroaches and just need to die...
But you shouldn't sugar coat or other wise use linguistic tricks to cope with the fact that you may have to take someone's life. Either accept it now, or deal with the mental consequences after the fact.