Distilled and Deionized water can all be totally different. Purified water is a broad term to use and can mean RO-Water, Chlorine water ect ect and normally is reference to drinking water.
Distilled water removes and kills allot of bacteria and other nasties in one go via steam / Pressure treatment. This is normal better than Deionized water.
Deionized water is simple filtered water then it is pushed though a bed of DI resin to "polish" the particles off. Its is not the purest of water and still has a lot of trace elements left over.
RO Water is better than DI and again it depends on how its made as there are many different types of filers. RO water is worked on a TDS% of what goes into the system and what comes out. E.g you could just have a simple RO system that produces 25 TDS water with only 3 filters or you could have a system like one of ours that has over 13 filters that remove heavy metals and many other types of filers, then goes though RO membranes then DI resin bed and finally a UV filers to produce 0 TDS water at source.
RO system can produce many different levels of water depending on what and how much is removed. There is a small issue though as the more you remove the more than can be sucked back in. So you have to balance out what you remove and even some times put back in certain chemicals or metals to balance it back out.
you can read up more on Wikis here ->
http://en.wikipedia.org/wiki/Purified_water
Storing water as well can impact on what you are getting. E.g storing water in leaching plastic bottles above 22c will see it increase its TDS rapidly. Water from car shops (local dealers not halfords) is normally better than Super store or Halfords water. Halfords water is better than super market water. Super market water is a pure gamble, we have seen it from 5us up to 30us (40 tds)