WillyCham - you're essentially correct, since the levels maintained in pools and in municipal water supplies are similar. Pools tend to be run with around 2 mg/L chlorine residual, while you'd typically see from 0.2 mg/l to 4 mg/L in your tap water. What you actually get at your tap depends on how close your are to the water plant and how your operators like to run the system. The major difference is that pool water will tend to have higher levels of chlorine byproducts, such as various chloramines (formed when you sweat or pee in the pool) and chlorinated organic stuff. I'm not sure how much of an effect these byproducts have on dive gear compared to "free" chlorine. In some places, they use monochloramine as a disinfectant, which is less reactive in chlorine and would probably be less harsh on your gear.
This next part gets into the weeds of chlorine disinfection and can easily be ignored
Them - you're essentially correct in your description of chlorine disinfection. To add to what you wrote, utilities that use gas chlorine typically draw the gas into a water stream under vacuum, where it reacts with water to form hypochlorous acid (HOCl), which acts as the primary disinfecting agent. Chlorine typically does not hang around as an elemental gas unless the pH is really low (below 3.5 or so, if I remember correctly). Some systems use high-strength bleach instead of chlorine gas for various reasons.
Also, while free chlorine will dissipate over a couple of days when left out, chloramines will not - they are much more stable in the water. So, if you decide to let water sit out a couple days to reduce chlorine, make sure your system uses free chlorine, and not chloramines.
SOURCE: I'm a drinking water treatment engineer and spent 2 years researching chloramine disinfection of viruses, and I've worked on gas chlorine and sodium hypochlorite system designs.