Validhunting is the hunting of players without a reasonable IC reason to do so. Players do not have to be attempting to kill another player to be considered to be validhunting. Validhunting is covered by the powergaming rules.
Non-Security
Non-security should generally not be focusing on seeking out, killing, or arresting threats. They can if threats present themselves, or if they are particularly relevant to the crewmember. For example, crew may attack a syndicate they see attacking another crewmember, and salvage techs may respond to a callout of carp in cargo. Certain severe emergencies may make it reasonable for normal crew to defend the station against it, like nukies or particularly destructive traitors.
Security
It is the job of security to deal with most sentient threats to the station. It is not validhunting for security to attempt to appropriately deal with these threats. Security being overzealous in attempting to deal with threats often falls under metagaming or inappropriate escalation, not validhunting.