The trappers came to the Island in search of rare animal skins and pelts. While some still hunt the rare animals, most have left the island or have been driven insane by the fog, as shown by the cannibal trappers in The Arrival who ate the synth trying to find his way to Acadia.
Although the reason for their insanity may be different, trappers are for all intents and purposes the Island's equivalent of raiders and behave virtually the same once combat is initiated. Just like the Commonwealth's highwaymen, trappers will attack on sight and their strongholds should be approached with caution.
What sets them apart to some extent is their lack of drug-addled taunting, something Commonwealth raiders are very fond of doing even when faced with impossible odds. Trappers also do not seem to care much about each other, given that they express no emotion whatsoever when they witness members of their group being killed.
Another distinguishing feature is the trappers' apparently complete lack of female members. While the ranks of Commonwealth raiders are made up of men and women in equal measure, the trapper population on the Island is entirely male.
The weakest of their members, basic trappers still should not be underestimated. They may be less resilient than their stronger comrades, but they often compensate their relative fragility with surprisingly powerful weapons like lever-action rifles and harpoon guns. If that is the case, they should be targeted first since they are the easiest to kill but can inflict great amounts of damage when left alone for too long.
The most experienced and, as the title suggests, most ruthless of their ilk, ruthless trappers tend to be the primary threat in any given encounter with trappers. They usually wear the heaviest armor and carry extensively modified weaponry which they use to deadly effect. Unless there are equally heavily armed but less resilient enemies around, dispatching them quickly before they can bring their superior equipment to bear should be everyone's first priority. While ruthless trappers typically serve as group leaders once they begin to appear, with increasing player level they gradually replace the other variants until trapper strongholds are populated almost entirely with ruthless trappers.
The three non-hostile trappers who are part of the quest The Arrival can be killed with impunity. When they respawn after a couple of in-game days, they retain their neutral behavior and will only attack in self-defense.