Loooooooong story (do a search online and you'll get pages and pages on it), but in short:
Superman and Superman II were shot as one big movie, over 18 months. As Superman's release date loomed, it was decided to concentrate on getting part one finished for the release date and then go back to part 2.
Anyway, as pressure mounted (Donner wanted to keep everything on scale and of quality, the Salkinds wanted a completed film with whatever effects work was done), there was a big falling out.
Donner was essentially fired from the project, even though an estimated 70% of Superman II had already been filmed. Donner's "pal" Richard Lester, who was also friends with the Salkinds from their previous Musketeers films, essentially knifed Donner in the back and, instead of being the mediator he said he was, schemed to remve Donner from the film and eventually took over.
Since DGA rules state that more than 50% of a film must be directed by the sole credited director, they threw out as little of Donner's stuff as they could and re-shot whole other scenes (the Honeymoon Hotel for instance).
Marlon Brando, who was always in the second but put an injunction out on them using his footage as he hadn't been paid for the first, left the project, as did Gene Hackman. Anything with Hackman in it is a Donner shot. They used a double for many of the Fortress Of Solitude moments at the end to get around him not being on set.
The rest of II was completed with shoddy matte work, and by re-using Williams' score (who also had left), adapted by Lester's friend Ken Thorne, who used a school-band sound instead of Williams' lush 110 piece London Symphony Orchestra.
Depsite some inspired (Donner) moments, Supes II is laiden with ill-judged comic bits from Lester and isn't nearly as good as it could have been.
Fans have been petitioning for years for a Donner Cut of Supes II, something WB says they are considering. There is so much footage out there that would make it a completely different film (alt opening and ending). The Eiffel Tower explosions that opens the film was tagged on. Originally it was the bomb on the rocket that Luthor sent into space from the first film that would have exploded and released the super villains from the Phantom Zone.
The films would have been much better interlinked, and its such a shame to see such a massive franchise become so mixed up.
Could have been soooo much better.