Bacteriostatic water vs sterile water
They look identical and cost about the same. The difference is whether the vial survives being used more than once.
Bacteriostatic water
Sterile water containing 0.9% benzyl alcohol. The benzyl alcohol inhibits bacterial growth, so the vial can be punctured and drawn from repeatedly over a period of weeks without the contents spoiling. This is the standard choice for reconstituting a multi-dose research vial.
Sterile water for injection
Plain sterile water with no preservative. Sterile at the moment it is opened, and no longer protected after that. Appropriate only where the entire contents are used immediately.
Which to use
For almost all peptide reconstitution work, bacteriostatic water is the correct choice, because a reconstituted vial is normally drawn from many times. Use plain sterile water only where a preservative would interfere with your assay.
Storage
Unopened bacteriostatic water is stable at room temperature. Once punctured, refrigerate it and observe the manufacturer's in-use period, typically 28 days.