In the US you can defend against force with an equal or lesser, but usually not greater, force. The categories of force are deadly and non-deadly. Also, you can respond to another in distress as if it were you in most instances -- called "defense of another" rather than "self defense."
If the attacker has a deadly weapon, such as a knife, you can respond with a deadly weapon, such as a gun. In many states, you will have to "retreat" if you have the option. Nothing requires you to be a marksman and only hit a limb, though. Take a pistol -- or rifle -- and try to pop a few rounds through a 25-ft. pistol target. It ain't easy. It would be quite a draconian legal requirement to make someone hit specific parts of an assailant's body.
The self defense laws in the US are about as good as they can be, IMO. I don't like the "must retreat" BS -- I shouldn't have to run from an assailant before I'm allowed to give him a third eye. The recent cases I've seen regarding the law in some European countries make me think the criminal has been given too many rights against the victim on the other side of the pond.
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