Here's the skinny from your science-gal:
Distilled water is also known as DI or deionized water. Water molecules have a slight charge to them. Distilled water is water that has gone through the process of removing the charge. You can purchase DI water in gallons from some stores, but you have to look for it. I used to have to buy it for work, and I was always able to find it at Kmart.
Bottled water is not DI water. There are also some differences in purity levels in bottled water. For example:
Spring water: is water that comes out of the ground on its own through a spring. It is bottled at the source and is not pumped from groundwater wells.
Purified water: Water that has gone through the process of being purified to remove chemicals, and basically anything else that would make it undrinkable. Purified water can be from fresh water or salt water. Usually the purification process involves a ritual chanting and sacrifice...oh wait...that's a different purification
The process generally involves reverse osmosis and other complex physical and chemical processes to remove impurities.
Filtered water: Probably isn't as safe to drink. Filtering is usually just the first step along the process of purification. Water is filtered in the environment by passing through a porous media such as sand. Sometimes this is enough to remove some impurities, but you don't really want to drink this kind of water unless you're out in the woods and in survival mode.
Mineral water: Either naturally or artificially, mineral water contains calcium, sodium, magnesium and iron. There are trace amounts of these in some people's tap water, which is why they may use a water softener. Water containing not less than 250 ppm total dissolved solids that originates from a geologically and physically protected underground water source. Mineral water is characterized by constant levels and relative proportions of minerals and trace elements at the source. No minerals may be added to mineral water.
Sparkling Water: Water that, after treatment and possible replacement of carbon dioxide, contains the same amount of carbon dioxide that it had at emergence from the source.
BOTTLED WATER:
By and large, bottled water is spring water and mineral water. Bottled water is subject to the requirements of the FDA and the EPA's Office of Ground Water and Drinking water.