Don,
Distilled water is basically water that is boiled and the steam is collected, condensed, bottled and sold. RO water is Reverse Osmosis, that is, it's water under pressure forced through a VERY fine membrane removing almost all impurities. DI water is De-Ionized water which is chemically filtered water. The only potential problem with distilled water is that some companies use copper condensation coils to change the steam back into liquid before bottling. Copper is not a good thing for reef tanks so you run a small risk of contamination. Reverse Osmosis removes between 95 and 99 per cent of the water's impurities while De-Ionization removes close to 100%. The drawback to "stand-alone" De-Ionization units is that the chemicals used to purify the water "foul" rather quickly, usually between 50 and 100 gallons depending on the quality of the water going into the unit. Now the DI media can be recharged very cheaply using heat and acid but it's a potentially very hazardous process, not to be taken lightly, leading us to the best of all (in many people's opinion, including my own) ... RO/DI this is simply a Reverse Osmosis unit which is plumbed directly in to a De-Ionization unit. By processing the water through the RO unit first, the water reaching the DI unit is almost pure, this increases the life span of the De-Ionization media greatly. All options are certainly viable and much better than using most tap water, the difference is cost and labor. If you don't mind lugging the bottles of distilled water back and forth, and you can verify that the distillery uses either glass or stainless steel condensation coils, it's fine. If your tapwater is not toooooo bad (most aren't) then a Reverse Osmosis is fine. If you don't mind spending money on replacing media every 50 gallons or so then De-Ionizations units produce, some believe, better water than RO. If you want the ultimate (at a cost) solution, then a 5 or 6 stage RO/DI unit is certainly the best you can do. Of course, the usual disclaimer applies, all of the above is just my opinion and I'm sure others will disagree with my oversimplified explaination but, none the less, hope this helps.
Later,
Paul