According to Chengkp75, who used to work on cruise ships, some are indeed actual salt water straight from the ocean as explained in his post last April: (https://boards.cruisecritic.com/topic/2844408-pool-water-on-celebrity/#comment-63001801)
"Salt water pools: The chlorine generating systems for land salt water pools are not accepted as being precise enough for use on cruise ships. If a ship with salt water pools is going to be at sea for more than a couple of days, they will simply pump filtered sea water into the pool continuously, and the overflow flows back to sea. The problem is that when the ship is within 12 miles of shore, it must switch to "recirculation", which stops taking in sea water, and merely recirculates the pool water, just like a land pool. In this mode, the pool must maintain a residual chlorine content, and this is done during the recirculation by real time chlorine meters, and metering pumps that add chlorine and acid as required, based on the bather load. When switching from "flow through" to "recirculation", the pool must be shut down until the residual chlorine level is reached, which is why the ships don't do it unless they have a couple of days of operation in flow through, as the passengers complain when the pool is shut down, and it also uses a lot of chlorine to re-establish the required level.
Fresh water pools: These are operated in "recirculation" mode, just as the salt water pools are, when the ship is within 12 miles of shore.
Many sea water pools still exist, and even newer ships use them, as it saves energy from making tons of fresh water that needs to be dumped weekly.
Further, it is not the salt that you smell in sea water, it is dimethyl sulphide produced by bacteria as they digest dead phytoplankton. The chlorine kills the bacteria, but the dimethyl sulphide remains."