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 homicide and may be manslaughter. An accident caused by carelessness may be negligent homicide. Sometimes, a death caused by someone else may not be a crime, for example killing in 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 fight in the war. Killing in self defense (if people being attacked kill the attacker) is usually not "murder".
Attempted murder is a crime. 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 a prominent person for a reason. The word is most used when the person who was killed was a celebrity or was a person involved in politics. The people who carry out assassinations are called "assassins" or "Hit-men". An assassin may murder someone for political reasons, for money, or for other reasons, such as favors owed and revenge.
The word "Assassin" comes from Hashishin, a Muslim group that was active in the Middle East from the 8th to the 14th centuries. This secret society killed people for political and religious reasons. It is thought that the assassins were under the influence of hashish and opium during their killings or during their training. The word assassin comes from either hashashim, the influence of the drugs, or hassansin, after their leader, Hassan-i Sabbah.