The premise is the same; Obito didn't come back to life at all, he simply entered Kakashi's subconsciousness after manifesting himself, similar to how Naruto's parents entered his. We know this because you see Obito talking to a much younger Kakashi instead of his now old self, though he did show up in some sort of spiritual state. During the entire exchange he transferred his chakra and eyes as well (the entire spiritual essence of Obito covering Kakashi prior to the dialogue in his subconsciousness.
It's an entire "beyond the grave" spirit type deal, Obito is very much dead.
The point was that during the transfer Obito transferred over his own eyes to Kakashi, thereby imbuing him also with all of the knowledge and powers of his eyes as well. Kakashi never had Sharigan eyes of his own, not to speak of Mangekyo -- it was Obito's the entire time. The difference is that when he got his eye the first time, he likely wasn't given much knowledge if any about how to use it, upon Obito's death. It's not a stretch to say that Kakashi will be able to do just about everything Obito could (outside of Rinnegan abilities), if he now has the very same eyes through this spiritual manifestation.
XI Wiki


