A lot of people are misunderstanding the terms in this story. Jutsu (Techniques) is not chakra, in a direct sense. The same exact logic applies to Senjutsu (Sage Techniques) and Sage chakra. Jutsu describes the techniques made available by using chakra, whereas Senjutsu describes the techniques made available by using Sage chakra. This same exactly logic still applies when we talk about Rikudou Senjutsu (Six Paths Sage Techniques), which is just a name for all of the techniques made available by using Six Paths Sage chakra.
If you can understand this, then it becomes obvious that Sasuke's Black Chidori, which in the past was Senjutsu fueled by Orochimaru's Sage chakra, was more recently Six Paths Senjutsu fueled by Hagoromo's Six Paths Sage chakra. The same goes for Kakashi, whose Chidori turned black after using Obito's Six Paths Sage chakra stolen from Madara.
Orochimaru makes it perfectly clear here:
If you can understand this, then it becomes obvious that Sasuke's Black Chidori, which in the past was Senjutsu fueled by Orochimaru's Sage chakra, was more recently Six Paths Senjutsu fueled by Hagoromo's Six Paths Sage chakra. The same goes for Kakashi, whose Chidori turned black after using Obito's Six Paths Sage chakra stolen from Madara.
Orochimaru makes it perfectly clear here:
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