We are both correct.Distillation is as you describe. The FDA does not specify that bottled water labeled as "distilled" actually be created through distillation though. They only require that it achieve the minimum level of purity associated with the result of distillation (it's the most pure of the bottled waters). Distillation is pretty expensive in terms of energy consumption, and often the same result can be obtained more cheaply through the use of better RO membranes, multiple passes through RO membranes, and use of DI resin. Most of the bottled water available as "distilled" isn't actually. It really doesn't matter though - it's still good.
Oh I agree with you and as is often the case, the labels are flexible.
I was just pointing out the differences with the processes. I do know in chemistry we would only use 'distilled' water ..we distilled it ourselves in the lab and tested purity with conductivity meters.
I personally feel that distilled water as labels should legally, be 'distilled' as there are differences in the water for those 'purity' reasons.
FDA basically just calls it 'purified' and gives the companies to much room to play with it.(just as long as it meets the minimum established guidelines)
