User with this ability either is or can transform into shinigami (death god), a "death spirit" of Japanese folklore who are responsible for seeing that a person dies at their appointed time and then guiding their spirit to be judged in the afterlife.
Shinigami are sometimes depicted as goblins or skeletal creatures who cause death and accidents, but more recent depictions of shinigami tend to be similar to western vampires, with them being portrayed as immortal, attractive people who wield a variety of unique powers. They will usually either cause death to sustain themselves, peacefully escort souls to the afterlife, slay demons and poltergeists who cause unnatural deaths, or be the result of unnatural deaths themselves. Or various combinations of the above.
The main differences between a Grim Reaper and shinigami are firstly that Grim Reaper is either a single individual or at least one of small group, while shinigami are generally both numerous and form a highly stratified and bureaucratic society of psychopomps and divine judges. The second difference is that shinigami as a whole tend to be weaker than a Grim Reaper: while some may reach impressive levels of power, average individuals are far below them.