Almost all of the worms people recognize in the hobby are bristleworms. That includes things like featherdusters and spaghetti worms. If you have a segmented worm in your tank, it's almost definitely a bristleworm.
The worms that sting when you touch them are all fireworms. The name applies to the entire family, Amphinomidae, not just coral predators. Most of the worms you would actually recognize as bristleworms are fire worms.
The bearded fireworm, (Hermodice carunculata) is a coral predator. It's extremely uncommon in the hobby and can be identified by the red tuft of "hair" on its head. If you can't tell if your worm has it, then it probably doesn't. It is diurnal, whereas most other fireworms are nocturnal, but in captivity it's not that useful for making an ID. Other worms will learn to come out during the day too when there aren't predators around and food is.