Everytime Superman goes back in time and alters the past, he produces a new iteration of the continuum. Besides, his same presence in the continuum automatically “branches” in two versions of him, where the one who alters the past then permanently disappears from existence once the change has been “sparked/set in motion”.
SUPERMAN: THE MOVIE
Superman 1: the one who travels back in time after Lois has died.Superman 2: the one who approaches Lois and Jimmy, both alive and safe, at the very end.
Superman 1 rotates backwards around Earth at tachyonic speed, and so travels back in time (NOTE: Earth does not really spin backwards, it’s just a visual representation to depict time travel). He comes back to the point where the missile has ALREADY hit the ground and the big wreck is just started. Basically, Superman 1 reaches Superman 2 and helps him lifting the Saint Andreas Fault better and faster (occurring off screen). This reduces and “reshapes” the earthquake path and its related damages to the point Lois’s location will never be involved so deeply and brutally as “it happened before” (Superman 1’s original timeline iteration).
We can only guess that Superman 1 and Superman 2 have eye contact underneath the Fault and Superman 2, being essentially identical to Superman 1, suddenly “theorizes” that Superman 1 must have come back in time for some uncertain and dramatic reason.
After the big struggle below the Fault, Superman 1 speeds up in the atmosphere in order to avoid any further contact with Superman 2, then rotates forward around Earth (occurring on screen) until he disappeares/vanishes/goes erased from the space-time continuum (occurring off screen). We don’t know why Superman 1 does the forward rotation, maybe he is able to briefly watch the future time again and thus know if his alteration has been successful, but quantic physics eventually catches up with him. Remember, he spent 12 years in the Fortress to learn all the universal knowledge and test his powers the best he could, so basically he is a scientist like his biological father.
After having saved many other people, Superman 2 approaches Lois and Jimmy, both alive and safe. Likely, all three people are feeling the deja vu effect depicted in the end of Superman II – The Donner’s cut. Jimmy mentions to having been saved by Superman (2) some time before, so some events played out like they did in the original iteration.
SUPERMAN II - The Donner’s Cut/Theatrical Cut
Superman 2: the one who comes back in time after the Fortress has been destroyed.Superman 3: the one who experiences the events of Superman II – Theatrical Cut.
Superman II – The Donner’s cut is set in 1979. At the very end of the movie, Superman 2 goes back in time. He destroys the missile some time before it would reach the exact point in space where The Phantom Zone Shard is fluctuating (inbetween Moon and Mars). That produces a third iteraration of the timeline. Superman 2 vanishes from existence. Superman 3 instead “goes on”… as far as we know, the two “Supermen” never have eye contact, so Superman 3 doesn’t know about the time travel.
The final scene in which Clark/Superman 3 teaches a lesson to the bully does not belong to the Donner’s Cut iteration, but to the Theatrical Cut. It can bee seen as the cinematic “proof” Donner himself suggested that the Theatrical Cut happened right after the Donner’s Cut.
After one year (1980), Superman 3 throws the booby trapped elevator in the space. The explosion causes the escape of the Kryptonian Renegades - the Phantom Zone Shard was fluctuating across our galaxy back and forth (in the same way as depicted in Supergirl) and it was trespassing the space inbetween Moon and Mars again. Superman II – Theatrical Cut occurs.