The NOTAR aircraft have a tail rotor, it is inside the tailcone, out of sight (and better protected, to be sure!)
The types of emergencies are the same, I would imagine, because the fan, its shafting, the control system for it, as well as the nozzel control mechanism are all subject to Mr. Murphy and his Law.
SilsoeSid you are also right to call into question the idea that an autorotation is the cure for all tail rotor failures. At high tail rotor pitch failure, an auto is the worst answer, possibly leading to loss of the machine (to say nothing about its occupants!) This is especially damning when, with a TR control failure to high thrust (so called "stuck left pedal") you could fly home first, and make a powered landing.