PhoenixRising

Well, in the original story from the comics it was the real Jean, and they killed her off by having her commit suicide when she realized that she might end up harming or killing Cyclops. This is why X-Men: The Last Stand made me angry, because Jean would never kill Scott, which is what the Dark Phoenix movie got right.

The reason they decided to kill off Jean was because writer Chris Claremont decided that Jean's genocidal actions made her irredeemable, so there was really no way to end the story other than to kill her off. Let's face it, other alien races would never stop wanting revenge on her. But then in the 1980s the new X-Men writers wanted to bring Jean back, perhaps because the Scott/Madelyne Pryor pairing just felt a bit forced considering she looked like she could be Jean's twin, or maybe they felt that killing off Jean was unfair, or whatever the reason was. So they retconned the story and made it so that the Jean Grey who emerged from the crash of the X-Men plane was not the real Jean at all. The real Jean was in a cocoon at the bottom of Long Island Sound, and the Jean that became Phoenix was a doppelganger created by the Phoenix Force, who duplicated all of Jean's physical characteristics and memories, including her personality. So because the Jean clone had Jean's memories, she also felt the same love for Scott and killed herself to prevent herself from killing him.

I know, sounds incredible, but that's what they did. The cocoon was first discovered by the Avengers, who later took it to Fantastic Four headquarters for Reed Richards to examine, and the Fantastic Four were the ones who ended up waking Jean up. Afterwards, Jean reunited with her old X-Men comrades who had all left the X-Men by that point. Beast had left the X-Men back in the 1970s and joined the Avengers, but had since left the Avengers. Iceman and Angel had also left, and for a time, the two of them, along with Beast, tried to form their own version of The Defenders, which was the team usually comprised of Doctor Strange, The Hulk, Sub-Mariner, and Silver Surfer. And Scott had left the X-Men after the Secret Wars, and losing his position as team leader to Storm. So once Jean was reunited with her old teammates, the original five X-Men - Scott, Jean, Hank, Bobby, and Warren - created a new team called X-Factor, where they posed as mutant hunters, but were actually using that as a cover to find mutants and help them learn to develop their powers before anyone else tried to capture them. This was also during the time when everyone thought the X-Men were all dead, but were actually just off-planet, and after returning to Earth, they were in exile in Australia for a while.