In Star Wars Episode 3: Revenge of the Sith (2005), you can see one B1 BattleDroid in the background telling his friend to look at Grievous activate his lightsabers.

The point Obi Wan was making is that Vader let go of his humanity in the process of obtaining those cybernetic enhancements. Considering Grievous is much further along that path and in the movies he doesn't get much character development, I don't think it's black and white.

While implants work one way in the real world, losing yourself is a core theme of Star Wars. After so much machining his body would need AI routines to enable the precise control needed to effectively use four lightsabers. When it comes time to fight, who's to say where that AI ends and the biological Grievous begins?

The correct term is obviously cyborg, but saying "no he's not a droid" and leaving it at that is not a useful response.

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