Organic stains — leaf litter, worm casts, anything that has sat on the surface — lift with chlorine. Metal stains, usually iron or manganese, do the opposite: chlorine oxidises the metal and sets the stain harder. The two require opposite chemistry, and there is no way to tell them apart reliably by eye.
Metal typically arrives with the water rather than from the pool. On a pool topped up from a bore or a tank, that is the likely route. It can also come from fittings corroding out of sight, which is worth knowing because treating the stain without addressing the source means doing it again.
Scale is a third category and a different problem again — calcium coming out of solution and depositing on tiles and surfaces. It is driven by hardness and pH, so removing it without correcting those means it returns.
Three categories, three treatments, and one photograph and water sample to tell them apart.