Serial murders are murders occuring at intervals, performed by the same murderer (perhaps with one or two accomplices). There is nothing to be gained by this - only the excitement a killer gets through such acts. Such a murderer has no political motive. He doesn't care what his victims believe, only that they have some physical aspect in common, usually. A mass murder is the murder of a large number of innocent people, killed in one single rampage. The murders in Norway by a single person would be a mass murder. A mass murder can also refer to a single instance of a large number of killings performed by some armed group or army. Chain murders usually refers to a series of murders performed by a government or political organization to silence those with whom they disagree and to terrify others who might be tempted to enter in to a confilict with the government. Such murders occur over a time and have a distinct political motive.