Board Thread:Episode Discussions/@comment-25319479-20171206103000/@comment-1512913-20171211113711

The original technique is Chidori, created by Hatake Kakashi the prodigy kid, son of legendary Konohagakure Shinobi, Hatake Sakumo the White Fang. Its name comes from the sound the technique makes, which is akin to a thousand of birds flapping their wings. One day, Kakashi supposedly cut a lightning bolt with Chidori and after that point, begun referring to it as Raikiri 'Lightning Cutter'

They are the same technique, just different names for it, with Chidori being the original name and Raikiri the nickname if you will.

Just for some reason, Raikiri is labeled as an S-rank technique, while Chidori as an A rank technique. This might be nothing more than an error, or it simply refers to the refinement that Kakashi has made to Chidori over the years, meaning that the base technique is an A rank, but super-focused version of it or whatever is S rank or whatever.