Chidori is The Same As Raikiri

[Xlad]

I think the real difference is concentration of chakra on the hand.

Chidori has more chakra

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Raikiri seemingly has more chakra

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[NeutralDjinn]

I think originally Raikiri is a more potent and better shaped for piercing version of Chidori, but Sasuke eventually improved his Chidori in a similar manner without changing the name.