the serial killer definition is a little more complex than just a person who murders multiple people.
Different authorities have different definitions with which to label serial killers. For instance, the FBI defines a serial killer as someone who murders three or more people over a period of a month or longer. To meet the FBI’s serial killer criteria, the culprit must have had a “cooling off” period in between murders, before deciding to strike again.
But the National Institute of Justice offers an alternative serial killer definition. It states that the killer must have murdered at least two people, motivated by a need for psychological gratification and with the act having sadistic sexual overtones.
According to an article on serial killers in Psychology Today, neither definition can perfectly capture all serial killers. They have varying motives and act under differing psychological states.