Modus operandi (method of operation, often shortened in English to M.O.) is a term used extensively in criminal investigations when discussing the methods employed by criminals. It refers to the personal habits of a criminal which form a recognizable pattern each time he commits a crime. The M.O. is the way that the predator commits the crime - for example, if he uses a gun rather than a knife - and his technique for the capture. The plural is modi operandi.
The term is also used in criminal profiling, where it can help in finding clues to the offender's psychology. It largely consists of examining the actions used by the individuals to execute the crime, prevent its detection and facilitate escape. A suspect's modus operandi can assist in their identification, apprehension, or repression, and can also be used to determine links between crimes.
While a serial killer's M.O. usually only differs slightly from time to time, his earliest victims may be killed in a different manner, as his preferred M.O. forms over time. In cases of serial killers with a large number of victims, there may be more out-of-pattern kills due to circumstances.
Signature is a ritual, something that the killer does intentionally for personal satisfaction and isn’t necessary to perpetuate the crime. Evidence of torture is a signature. Dismemberment is a signature. Posing or displaying the victims in a certain way is a signature. Signature is a way of linking cases. Like a real signature, it’s a personal detail that’s unique to the individual.
While the modus operandi tells how he did it, the signature gives insight into why he did it.