Murder is:
1. Deliberately killing a particular person, without justification.
Example: a man is angry that another man has damaged his property. He takes a gun and shoots him.
2. Deliberately killing any person without justification.
Example 1: a terrorist plants a bomb in a shopping centre, it explodes killing several people.
Example 2: a man is angry that another man has damaged his property, he takes a gun a shoots a person, but it turns out to be someone else.
Murder may be:
3. Committing a crime, in the course of which someone is killed ( Felony murder ). Applies in some countries only.
Example: a man robs a bank, a police officer dies chasing after the robber.
Murder is not:
4. When a person kills in the belief that he is acting lawfully to defend himself and/or others.
Example 1: a man hears a burglar enter his home at night. He takes a gun and shoots the burglar.
Example 2: a man thinks he hears a burglar enter his home at night. He takes a gun and shoots the person, but it turns out the person is not a burglar.
Example 3: a police marksman shoots a terrorist in the belief that the terrorist is a danger to the public.
Example 4: a police marksman shoots an innocent man in the wrong belief that he is a danger to the public.
5. When a person kills someone without meaning to.
Example: a driver fails to see a pedestrian and runs him over.
In cases 4 and 5 there may still be a crime (manslaughter), if the killer was negligent in not acting with sufficient care, reckless behaviour, but it is not murder.
Note: the belief/intention of the killer is important, as well as the physical act, this idea is referred to by the Latin term “Mens Rea” meaning “the act is not culpable unless the mind is guilty”.
Reform / difficult cases
From https://en.wikipedia.org/wiki/Self-defence_in_English_law#Reform
The Law Commission’s report on Partial Defences to Murder rejects the notion of creating a mitigatory defence to cover the use of excessive force in self-defence, but accepts that the “all or nothing” effect can produce unsatisfactory results in murder cases. For example, a battered woman or abused child using excessive force because they are physically at a disadvantage and not under imminent attack, would be denied a defence. Further, an occupant not sure if violence to defend their property against invasion is reasonable, may feel forced to do nothing. It was always possible the same set of facts could be interpreted as either self-defence or provocation where there was a loss of control resulting in death. Thus, the Commission recommends a redefinition of provocation to cover situations where a person acts lethally out of fear. This reflects the present view of psychiatrists that most people act in violent situations with a combination of fear and anger in their minds, and to separate the two emotions is not legally constructive.
Conclusion
Someone subjected to unlawful threats, and who kills out of fear of future violence, should be charged with manslaughter and not murder, where their actions were not entirely lawful. Sentencing should fully take into account the level of provocation and steps the accused person took to lawfully resolve the situation before killing out of fear.
See also What is Murder ?