BWSL is the company responsible for the distribution of city water, which is produced at the desalination plant owned and run by Consolidated Water Services.
Some properties have well water, some have cistern water, some have city water and some use a combination.
If you are drinking city water, it is potable. Some also drink cistern water - I think it depends on how well you maintain your cisterns. Whether you receive city water, cistern water or well water will depend on when, where and who developed the property. Piped city water is not available on some parts of the island.