Culpability and the exact crime actually depends a LOT on your mental state and what intent you supposedly had. Let's start with some basic cases and get weirder:
* Intent to kill or harm someone - murder (with degree being dependent on how much pre-meditation you had)
* Intent to pull the trigger, but not to kill or hurt anyone - manslaughter
* No intent to pull the trigger (eg accidental discharge - maybe the trigger pull on the gun is very light and you put a little too much pressure on it) - possibly manslaughter on recklessness grounds if you knew there were people around or the person was there, but also maybe a lower crime (or not a crime at all) if you were being careful with the gun and got unlucky about where it was pointing when it discharged
* Not mentally competent to understand that you might be hurting someone or that hurting someone is wrong - not guilty because of insanity
* Intent to kill the person in self-defense and the person is intending to kill or harm you - not guilty of any crime due to self defense (a murder, but not a crime)
* Intent to kill someone else who is attacking you in self-defense, but you missed - also self defense (intent follows the bullet)
There are probably 10+ more other major scenarios to cover here with different outcomes. This is partly why when someone kills someone else with a gun, the prosecution tries to hit them with murder, manslaughter, and reckless handling of a deadly weapon. They don't know which one will stick, but they can be pretty sure that a jury will find one kind of intent.