The stains on the stone are around the waterfall feature and would get wet. The tile stain is above the water line. However, this is an underground hot tub (though we never heat it). So any wind can kick the water above the "waterline".
Without test results, it's a bit of a guess, but it looks like calcium deposits. A mixture of 3:1 water and muriatic acid will get most of it. Apply the mixture and, if the stains foam up, it is calcium. rinse after cleaning.
Those aren't metal stains in the usual sense, though there may be some iron involved. Looks like efflorescence to me. Presumably caused either by water either seeping through the wall or moisture from the pool running down the wall.
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