Murder is when one person kills another person on purpose. It is only called "murder" when it is against the law. If a person does something that makes someone else die, it is often known as manslaughter or homicide. This is true if it was an accident. Sometimes, a death caused by someone else may not be a crime. For example, in some situations, killing may be self-defense. A person who commits murder is called a murderer.
The legal definition of "murder" and "manslaughter" may be different in different countries, and is very much argued on: for example, killing in war is not usually called "murder" by those who take place in the war. Killing in self defense (if people being attacked kill someone who is attacking them) is usually not "murder".
Attempted murder is a crime in England, Wales, Northern Ireland, states in the USA, and in other jurisdictions. Attempted murder, or "attempt murder" in common law countries, is when someone tries to kill another person. Just planning a murder is not enough. The act must come close to, but does not actually take the life of the other person.
"Assassination" is a word which means murdering someone for a reason. The word is most used when the person who was killed was a famous celebrity or was a person involved in politics.
Murder for Kids. Kiddle Encyclopedia.