Actually I think there is one other non planetary object that is known to have a ring but I can’t remember the name of it right now.
And this is why asteroids and comets should be segregated. First you get a comet with a ring, then you get an asteroid with a tail. Then you’ll have objects with tail rings, ring tails, ...it’ll be complete chaos!
Well, what makes a comet a comet? The orbit is elliptical, and it gets the tail flowing out from it as it travels close to the sun. An identical object in a circular orbit far from the sun would never have the tail so it really could never be called a comet.
An asteroid is only an asteroid because it is in a circular orbit around the sun. Orbiting any other body, it would be called a moon of that body. Diemos and Phobos are both tiny rocky objects that really look a lot like asteroids. Some of the moons of Jupiter and Saturn are icy objects that probably would be comets if they were in the right kind of orbits.
Chiron is a lot like Pluto but orbits much closer to the sun. It might have been termed a planet for a while had it been discovered sooner. And any of these objects would be called comets if they passed closer to the sun.