Chlorine in chlorinating compounds (hypochlorite, dichlor, trichlor, cal-hypo) is reduced into chloride ion (Cl-) and measured as salt build up. All chlorinated swimming pools build up chloride ion over time. Muriatic acid (hydrogen chloride) also adds chloride ion to the water while dry acid (sodium bisulfate) leaves sulfate ions behind. Dichlor and trichlor add cyanuric acid as well as chlorine and cal-hypo adds calcium ions in the form of carbonates and hydroxides. Alkalinity increaser (aka, baking soda) and pHUp (soda ash or sodium carbonate) adds sodium ions and carbonates to the water. Sodium doesn't matter at all because it remains in solution and will not scale out at any normal pH. Carbonates and bicarbonates vary in concentration with dissolved CO2 and atmospheric CO2 depending on pH and the outgassing rate of CO2 from the pool to the atmosphere. All pool water is over-carbonated relative to atmospheric CO2 levels (think of the pool like an opened soda can) and so CO2 is constantly outgassing to the atmosphere. This is the reason why pH is always increasing in most pool water. Bathers leave behind salt from sweat and urine as well as organic compounds that breakdown from chlorine oxidation into simpler organics. Nitrates and phosphates build up over time and, while phosphates can be removed if the pool owner wants to do that, nitrates can not be removed and simply build up in the water.
In my area of the country where water is scare and we try not to lose a lot of it out of our pools, pool's eventually need to be drained and refilled. In wetter climates where rain and winter snow is plentiful, there's enough water exchange to typically keep pool water balanced without any full draining required to removed dissolved solids and salts.
Total dissolved solids (TDS) is the old test method pool operators used to determine the buildup of chemicals in pool water. However nowadays, with modern test kits, pool owners can test for each specific chemical level in water and know it's concentration rather than some unspecific total value.
