Reapers in general are far stronger than mortals and are immortal though they can be killed depending on circumstances. Their weapon depends on what they prefer, such as Grell and his chainsaw.

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The Head Reaper keeps the others in check and interferes when Lady Fate requires him to.

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Shinigami are somewhere between a god and a reaper and there are two kinds, the dark and the light.

Shinigami like those from Death Note are Dark Shinigami and wreak havoc, creating hallows from those whose names they write in their notes. After the Shinigami war, they were kept to their sector, a dry and seemingly endless wasteland between Earth and the soul society.

Shinigami like those from Bleach are Light Shinigami, and work to defeat said hollows and aid souls on their passage to where they must go. They carry Zanpakutō, swords that are the vessels for spirits.

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The Grim Reapers are the well-known ones and usually stick with a few select souls for all time unless they fall in which a new one must be chosen.

If someone manages to kill a Grim Reaper then they take their place, forgetting all human memories unless they have a strong mind in which a few memories remain.