Originally Posted by
Wiccan
Phoenix!Jean is really Jean. She's honestly no different from the current Krakoan Jean, in the sense that she's not Jean's original body or mind but a perfect copy of it. The only difference is that back in the 80's the narrative went with the idea that it didn't count as her, while the current era says the mutants resurrected through the protocols do count as the same person.
The Classic X-Men backup that shows how it actually happened, introduces the idea that Jean's soul was divided, a part of it in her original body and a part of it in the new one. You see Jean's dialogue seamlessly transition from her old dying body to the new one made by the Phoenix. And then in Inferno, they also introduce the idea that after Dark Phoenix's death, the missing part of her soul was supposed to go back to her original body in the coccoon, along with all the memories, to make Jean "whole" again, and she should've come back remembering her time as Phoenix.
To me this was all clearly Claremont's way of trying to make his Jean count, as much as he could with the retcon that editorial was enforcing. Even after Simonson wrote the story where Jean expels the Phoenix shard and loses the Phoenix/Madelyne's personalities, and says that the memories were now distant and not really like her, when Claremont got into X-Factor again he went and wrote a scene where Jean is in the moon and says something like "It shouldn't, but the memory it's mine, and it's real, I remember with every fiber of my being, this is where I died!", establishing that she actually does remember her Phoenix self as if it was her.
I think at least part of the problem is that, back at that time, the writers didn't quite make a differentation between Phoenix as in Phoenix Force, the cosmic entity, and Phoenix, the Jean Grey "clone" that hosted the force and went by Phoenix. They acted like it was just the Phoenix "impersonating" Jean, when in reality, it was still the Phoenix Force inside a host.
Now, Madelyne: The fact that she only woke up with the part of Jean's soul that was missing does help make a case against her. But even after Jean reabsorbed that, she has managed to come back, meaning she does somehow still exist as a separate person. Besides that, she had her own set of memories (fake, but still) and a different personality, not to mention her own life experiences from the moment she was created to now.
TLDR: Phoenix!Jean from Phoenix Saga is Jean. Madelyne is not.