The ending of Batman Returns settles the Penguin and Shreck for good, but deliberately leaves Catwoman open: she survives, refuses Bruce, and is last seen alive beneath the Bat-Signal.
Batman defeats the Penguin's plan and the villain dies from his injuries. Shreck is killed in a confrontation with Catwoman. Bruce then finds that Selina is Catwoman and begs her to come home, but she refuses and he is left alone. In the last scene Catwoman is seen alive, looking up at the Bat-Signal.
The Penguin's endgame is the darkest stretch of the plot. After dropping the mayoral disguise he plans to kill the first born sons of Gotham, and when that fails he turns to a missile attack carried by an army of penguins. In my opinion, that sequence is what separates this sequel from batman 1989, where Batman faced one villain in the Joker. Here the Penguin's grievance, abandoned as a baby and raised in the sewers, is aimed at the city that never looked for him, so Batman's win feels less like a triumph than a clean up.
Selina's arc mirrors his. She is the timid assistant who overhears Shreck's plans, is pushed to her apparent death and comes back as Catwoman. Shreck dies at her hands, so her revenge is paid off, yet she still turns Bruce down. It could be argued that this is the film's real tragedy: Bruce spends the story romancing Selina without knowing she is Catwoman, and he finishes it alone.
Why does Catwoman not like Batman in Batman Returns? Selina and Bruce are romantically involved without knowing each other's second identities, while Batman and Catwoman clash in costume. When Bruce learns the truth he begs her to come home, and she refuses, with no reason stated. That refusal is the most honest beat in the film, because it denies Bruce the tidy reunion.
The final shot matters for the franchise too. Burton began developing a Catwoman spin-off for Pfeiffer, which is why Catwoman does not appear in batman forever. There, Bruce is instead drawn to Dr. Chase Meridian, so the open door Returns leaves for Selina is never walked through. Is Batman Forever a continuation of Batman Returns? It follows in the release order and keeps Michael Gough and Pat Hingle, but it has a new director in Joel Schumacher and a new Batman in Val Kilmer.