Oy. Fireworm and bristleworm are completely interchangeable umbrella names for a VERY large group of animals called polychaet worms. There are literally thousands of species, all of which can be called either fireworm or bristleworm.
Now, there is at least one species that is a bit more specific. The Caribbean Bearded Fireworm. It eats gorgonians, is diurnal, and is completely fearless. And you don't have one.
The Bobbit worm is predatory and ambushes small fish swimming near the sand. That's not what you have either.
What you have a generic, beneficial bristleworm. They do not kill and eat fish, unless they are huge and starving or the fish is severely sick or injured already. They do not munch on coral (a few notable exceptions, see above) but may eat detritus OFF the corals, or crawl between them. Contrary to popular belief, this motion does not stab the coral with bristles (worm bodies simply are not designed for that motion), so other than being a little annoyed, the coral is generally left unharmed.
The one situation in which you can absolutely count on bristleworms to eat fish/coral/anemone/etc is if the fish/coral/anemone in question is already dead or dying.
A healthy, thriving, diverse population of bristle worms is the single most beneficial thing you can have in a saltwater aquarium.