Does the defender shoot to kill,, shoot to wound, or what?
My answer is, neither; that you shoot to stop.
However, the best way to achieve this is through a hit in the central nervous system or the heart or aorta. The hit to the CNS will usually have instant results, and the hit to the circulatory system will usually be very fast, but sometimes not instantly.
Sadly, the shots that will disable instantly, are very often fatal. Even if your foe does not die, the purpose of shooting him will have been met.
NYPD has had this (shoot to stop) as their doctrine for years, and it has served them well.
Please keep in mind that the purpose of defensive bullets is not to kill; it is not to wound. Their only purpose is to stop the bad guy. To paraphrase something that I read a long time ago: killing the bad guy is not your job; it is a function of the courts. That your bullets kill is simply a regrettable side effect. Their function is to STOP whatever action forced you to shoot in the first place.
The use of deadly force in self-defense is to stop a deadly threat to you or someone that you are responsible to protect, and that is it's only function. Killing should not be your goal, but since stopping the threat may very well result in the death of your adversary, you should never shoot unless you are justified in killing him (or her).
Keep this in mind and you will be less likely to get in trouble.
And I agree: In the Gravest Extreme is a classic book, and one that I recommend very highly.