Total Dissolved Solids (TDS) refers to chemicals in pool/spa water that remain as solids after evaporation of the water. One method of measuring TDS includes doing such boiling/evaporation and weighing the resulting solids. This method will remove any dissolved gasses, but also removes volatile chemicals and chemicals that can convert to gasses when concentrated, such as some of the carbonates (e.g. carbonic acid which is a combination of carbon dioxide and water).
However, TDS is usually measured through an estimation process that uses an electrical conductivity meter. This measures the quantity of charged ions in the water, but for this method to be accurate one must have some idea of the kinds of ions in the water. The conductivity will be related to the nature of the ions and especially to their charge since the conductivity is roughly proportional to the charge. Also note that TDS is measured in parts-per-million (ppm) so is affected by the atomic weight of the chemical. Because conductivity is being measured, any neutral molecules will not get counted towards TDS including urea, cyanuric acid (as opposed to cyanurate ions), hypochlorous acid (as opposed to hypochlorite ion) and boric acid (as opposed to borate ion).
In a typical pool that does not have added salt for a saltwater chlorine generator (SWG), the TDS mostly comes from the chemicals added to saturate the water with calcium carbonate to protect plaster surfaces. These include calcium chloride and sodium bicarbonate. Some amount of calcium (CH) and bicarbonate (TA) are usually in the fill water already. At a pH of 7.5, TA of 80 ppm, CH of 300 ppm, the initial TDS will be about 500 ppm assuming most of the CH is added by calcium chloride. As chlorine is added to the pool, its usage/consumption results in chloride ion and after adjusting for pH (if needed) there is usually sodium ion as well so the net result is an increase in sodium chloride salt. So for most pools, the largest component of TDS is this salt.
So TDS by itself is a pretty useless indicator. It roughly tells you the amount of salt in the pool, but there are specific chloride tests (that use ppm sodium chloride units) that would generally be more accurate. Since the primary increase to TDS comes from added chlorine, the TDS can sometimes be used as a rough proxy for the "age" of the water, but this requires further information to be useful. Obviously, if a pool is not used (i.e. no bather load) and has no blown-in organics, the increasing TDS simply means the pool is getting more salty. There will be no side-effects in terms of disinfection or oxidation, though the saturation index will drop somewhat (by about 0.2 going from 500 to 3000 ppm) if all other parameters remain the same.
In a commercial/public pool with high bather load or in a pool with a lot of blown-in organics, the TDS or salt level can be more useful since some organics from bather load or that are blown-in are not easily or fully oxidized. These chemicals can build up and have side effects in the water mostly seen as an increase in chlorine demand though sometimes seen through foaming, precipitation, s c u m (spaced to avoid profanity filter) lines, etc. that occurs after water becomes saturated with the chemical. However, so long as the Free Chlorine (FC) level is maintained, there are no effects of these other chemicals on disinfection or oxidation other than the extra chlorine demand already noted. It would be better to simply keep track of the cumulative bather load relative to the water dilution, but since the bulk of chlorine demand in high bather load pools comes from the bather load, the salt build-up can be a useful proxy. Just remember that the rate of such salt build-up depends on the source of chlorine.
There is one important exception to what was just described. If stabilized chlorine is used, then there is often a build-up of Cyanuric Acid (CYA) and this significantly affects the rates of disinfection and oxidation. If the FC level is not proportionately raised with the CYA level, then algae can start to grow and the chlorine demand can rise even before the algae becomes visible. The water can start to turn dull or cloudy as well, both from algae growth and from a build-up of organics that are more slowly oxidized due to the lower active chlorine levels. In fact, the primary reason that TDS gets blamed for pool water problems is that the CYA has built-up, but instead of laying the blame correctly to CYA, it is TDS that is claimed to be the culprit.
It is possible for some organics to have a CYA-like effect of binding to chlorine but not measuring as Combined Chlorine (CC) in tests (i.e. still measuring as FC). If ORP is low in spite of a proper FC/CYA ratio, then this can indicate this CYA-like effect, though ORP is also affected by other chemicals so a specific hypochlorous acid sensor would be a better indicator for the CYA-like effect.
To the extent that TDS is a proxy for the cumulative bather load, then it can give some indication for the need for some water replacement, but it is usually much easier to simply measure the base chlorine demand to get an idea of what is going on in the water. The base chlorine demand is measured when there is no sunlight and no bather load, so is usually done overnight. If one measures the drop in chlorine without the pump running, then this gives a rough indication of the amount of organics to oxidize in the bulk pool water. If measured with the pump running, then this adds the amount of organics in the filter (as well as bacterial biofilms) that also contribute to chlorine demand. In high bather load pools that are indoors, there is usually a significant build-up of urea in the water and this is often the primary component of the no-bather no-sunlight chlorine demand. Outdoor pools exposed to sunlight also build up urea, but at a lower rate possibly due to the UV breakdown of chlorine producing free radical chain reactions that help oxidize urea more quickly (this is my speculation).
So if the chlorine demand gets higher and appears to be due to chemicals in the bulk pool water, then water replacement is the typical solution though one can also use enzymes or supplemental oxidzers (e.g. non-chlorine shock, ozone). According to ANSI/APSP-11, the standard water drain and replacement rate for pools is 7 gallons per bather which is probably per bather-hour assuming a typical 1 hour bathing time in pools. For spas, the Water Replacement Interval (WRI) for a complete drain/refill is (1/3) x (Spa Volume in U.S. Gallons) / (Number of Bathers per Day) where it is probably assumed that soak time is 20 minutes in a hot (104ºF) spa so should be scaled accordingly.
Finally, a very high TDS implies a very high salt level. As noted earlier, this affects the saturation index, but it also implies the potential for problems associated with high salt level itself. This includes greater risk of metal corrosion due to increased conductivity of the water and, for stainless steel, the higher chloride level inhibiting reformation of the passivity layer and greater risk of destruction of soft stone from salt splash-out, evaporation, and recrystallization.
In theory, an ORP system should record a lower reading at higher chloride levels in the pool so that would be consistent with what you have been seeing. However, some ORP manufacturers claim there is no correlation with ORP and chloride (salt) level (see Figure 9 in this file). It sounds like perhaps they are wrong and the theoretical science is right. In theory, every doubling of chloride concentration would reduce the ORP by 9 mV, but chlorine itself should also follow this relationship but doesn't. It varies by sensor, but is often in the 20-30 mV per doubling of chlorine concentration. So if chloride tracked similarly to chlorine, then doubling the chloride concentration might end up with doubling the FC to maintain the same ORP level. That sounds roughly like what you've been seeing.
Of course, one can simply adjust their setpoint which is really all that ORP is good for anyway since it's just process control for an FC level by using a setpoint. The absolute ORP level varies so much by sensor manufacturer and model even measuing the same water that using an absolute ORP reading by itself isn't of much value, especially if one understands the FC/CYA relationship when CYA is used in the pool (i.e. knows that hypochlorous acid level drops when CYA is present). ORP is a rough proxy or guide to hypochorous acid concentration, but a selective membrane hypochlorous acid sensor would be better. Unfortunately, such sensors have been unreliable in the past.
By the way, for an ORP device such as Oakton, 700 mV ORP would be around 0.3 ppm FC with no CYA while for Chemtrol it would be around 0.1 ppm FC with no CYA. Most sensors should report roughly in the 790-810 mV range for 3 ppm FC with no CYA, but as I noted sensors vary a lot where as noted in this post 23% of pools with two sensors varied by 100 mV or more in their readings of the same water.
I'm not saying that ORP isn't an absolute measure at all, but that it is not a RELIABLE absolute measure because of the large variations that are seen. It is far better as a process control tool since for a given sensor over a moderate period of time it is able to roughly track the hypochlorous acid concentration. However, the ORP reading can not only drift over time due to TDS (probably chloride in spite of what Chemtrol says) or temperature or pH or sensor degradation (needing cleaning), but also due to hydrogen gas bubbles from a saltwater chlorine generator and from ozone from an ozonator (though in this latter case it's measuring legitimate additional oxidation and disinfection capability, but is very dependent on ORP sensor placement since ozone is relatively short-lived).
So you are right that the key is to accurately measure the FC and CYA levels and set a setpoint ORP mV based on your desired goal and periodically remeasure and adjust the setpoint as needed though it's probably not that frequent -- weekly resetting is probably fine though by code you've got to be checking your FC levels multiple times a day anyway. Try to keep the pH fairly constant through other means or else you will get swinging ORP that will cause swings in FC. Keep the ORP sensor away from returns to avoid feedback problems, especially if an SWG is used since you don't want the hydrogen gas bubbles to interfere with sensor readings. Hydrogen gas will lower the ORP reading. I don't think that TA and CH levels play any direct role in the ORP reading so you just manage those separately. Once you've got things stable, then ORP can be used to keep the hypochlorous acid concentration roughly constant even in the presence of bather load and that, after all, is its primary function.
I just don't want people to get the idea that an absolute reading of ### mV actually means anything that accurately. As an absolute measure, it's not very good (not meaningless, just not that accurate), but as a relative measure for process control it is useful.
I always install my ORP systems to take my sample readings near the pump & before the filter to read the water coming back from the pool. As long as the return inlets aren't too close to the suction, I think I'm reading the "dirtiest" water in the pool. I always inject sanitizers, either ozone, salt chlorine or liquid or tablet chlorine the last thing before the water goes back to the pool.
I agree that TA & calcium don't affect the ORP, but after following the threads by Mr. Skinner & the NPC issues, I'm looking for the most even handed and gentle way to sanitize pools that have a medium to high sanitizer demand, and these parameters are critical for that. Too many pool guys go weeks & months before checking & adjusting these things, even on semi public pools. That is why I am so glad to see TDS issues addressed here.