Filtering removes whatever the filter is designed to remove. Some remove odors, some remove bacteria, some remove iron and other metals and some remove chlorine, flouride and other crap. Just check the specs of your filter model. Distilled water comes from heating it to steam and it condensing into water again. All the polutants get left behind because they do not change state into a gas like the water does. Personally, I just use tap water and my grow has been fantastic and I know a lot of other growers who are getting away from the pricey bottled water or RO water. I spent a lot of money last year on water; not so this year and my results are just as good.