I was under the impression they were the same thing and after some research, it appears to be the same jutsu under the guise of two different monikers but its true name is chidori.
Now if you delve deeper, there are technicalities that Raikiri is the stronger version as when Kakashi grew stronger with the sharingan he was able to turn what was essentially an A ranked jutsu into an S ranked one, but its... Still... The same thing...
I guess its like Rasengan. They're all the same thing, just with different versions and strength. Idk. I always considered Raikiri and Chidori the same thing. And they are. At least with rasengan they're not only visually different but different in size and stuff. Raikiri is just Chidori but lightning-y-er... So after my full conclusion, Raikiri is the stronger version, but at base its the same exact thing, concept and all.