Most bottled spring water isn't chlorinated and is sanitized using ozone and UV light, neither of which leave any kind of taste residue. It is then filtered through carbon filters, and sometimes reverse osmosis, before being bottled. The tap water on board is treated heavily. If you are used to a certain brand of water - Evian, Voss, Fiji - you will find the tap water on board very flat in the mouth but with a noticeable residual treatment taste.
The tap water also has to run through miles and miles of sometimes old ship plumbing and tanks. And sometimes that plumbing doesn't work so well.
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Personal preferences aside, drink plenty of clean water. We don't see many doing it on board, and sometimes taste is one of the reasons. Not that you have to drink water, but we like to. Low water consumption can lead to all sorts of problems - particularly when substituted with sugary stuff - so we like to use any incentive that we can find to drink it!