Distilled & Deionized water is generally considered "pure".
Water used in Batteries should be free from Disolved Solids* (salts, chlorine, calcium, magnesium, and iron compounds).
* A purity of less than 50 ppm TDS is often recommended. Total Dissolved Solids (TDS) is the measurement of the quantity of a solid dissolved in water ,in parts
per million (ppm). A purity of 50 ppm is roughly equivalent to a conductivity of 100 μS/cm (micro-Siemens per centimeter). A "disolved" solid cannot be filtred by conventional means.
When a cell gasses the water evaporates and escapes. Any solids within the water cannot evaporate, and simply fall to the bottom of the battery. To replace the water that has evaporated more water must be added, and with it comes a new batch of dissolved impurities, which also fall to the bottom of the battery when the water dissolves.
This continual process builds cumulative
deposits of impurities in the bottom of battery, and mossing and dendrite growth on the separators. Chlorine bleaches separators. Calcium or calcium carbonate neutralizes the battery acid (electrolyte).