Special Circumstances in the Law, Crime Fiction, and Daily Life

First of all, some definitions, taken and slightly adapted from Wikipedia:

Special circumstances in criminal law are actions of the accused, or conditions under which a crime, particularly homicide, was committed. Such factors require or allow for a more severe punishment.

Special circumstances are elements of the crime itself, and thus must be proven beyond a reasonable doubt during the guilt phase of the trial. As such, they are formally distinct from aggravating circumstances, in that the latter are proven during the penalty phase of the trial instead.

One example of element of the crime: For murder, the mental element requires the defendant acted with “malice aforethought” [planned, intentional].

Aggravating circumstances are elements that make the crime graver. Examples include hate crimes or “use of a deadly weapon.” Mitigating circumstances are those which make the crime less grave (the opposite of aggravating).