I'll try to clear this up to the best of my knowledge.

Chidori = 千鳥 (thousand birds)
Raikiri = 雷切 (Lighting slice)

And we all know that when Kakashi first used Chidori, Kishi named it Raikiri. It was later explained that the name of the move (created by Kakashi) was Chidori, and that Raikiri was a nickname for the move. So, it's not hard for us to relate to Chidori as a lightning elemental move.