The only real difference is the preservative
Sterile water for injection is water that has been sterilised and contains nothing else. Bacteriostatic water is the same water with approximately 0.9% benzyl alcohol added as a preservative. Benzyl alcohol does not sterilise; it inhibits the multiplication of bacteria that are introduced during repeated stopper punctures.
That single difference determines the use case. A vial reconstituted with sterile water is a single use preparation, because any organism introduced at first puncture will grow. A vial reconstituted with bacteriostatic water tolerates repeated withdrawal over a defined window — conventionally around 28 days under refrigeration — because introduced organisms are held in check.