What society would eventually know as serial killing was originally thought of as "thrill killing", "stranger-on-stranger murder", "recreational killing", "pattern murder" and numerous others. There wasn't an exact name for what investigators were seeing at an alarmingly increasing rate. In fact, it wouldn't be until May 1981 before serial killer and serial-murder constructs were printed in mass media while they covered the breaking news story of Wayne Williams. Williams had been suspected of killing 31 children in Atlanta 1979 to 1981.
In the 1980s, the term serial killer was defined as having 3 victims on separate occasions with a "cooling-off" period in-between. However, this quickly revealed that the 3 victim definition provided all sorts of statistical and conceptual problems. It excluded murdered who had an obvious and identifiable serial-killer psychopathology but were apprehended after their first or even second murder before they could commit more. It also did not account for the serial offenders who only had 2 convictions which caused for some notorious serial killers such as Albert Fish, Ed Gein, Albert deSalvo and Wayne Williams to be excluded from the 3 victim definition as well.
There are some basic classifications of serial killers including organized, disorganized, and mixed categories. Thank you, Mindhunter for gracing us with some insight on criminal profiling!