Well I understand.
But the only way Deidara said. And Sasuke fix it, saying that he Chidori.
C said that the techniques are similar.
I don't remember more cases.
It essentially does not change.
Raikiri personal Chidori is Kakashi.
To make it clearer.
Two absolutely identical in all knife called "knife".
The first killed 500 people, slightly improved and named "Killer"
The second nobody was killed.
Both are "Knife", but only one "killer"
And from them. Both Chidori, but Kakashi Chidori is Raikiri. Because he has improved it, and cut them lightning.
It also tells us and databook
"When Kakashi uses it, "Chidori" is known as "Raikiri".
"Kakashi's "Chidori" cut lightning...that legend is the origin of the
name "Raikiri"."
No. Databook => Manga
Kishimoto not just like that it wrote it.
It serves for the explanation of various moments, and placing of all points over i.