According to the FBI, an individual actively engaged in killing or attempting to kill people with a firearm.
An individual with a weapon is not an active shooter if they have not pulled the trigger.
Until a shot or shots have been fired, think suspect, man with a gun, woman who may have a gun.
The designation exists to alert law enforcement to “an aspect of the crime [that] may affect the protocols used in responding to and reacting at the scene of the incident.”
Note there is no hyphen.