I'm no water expert but don't you mean de-ionised?
Distilled water is pure water with 99.9% of the minerals, bacteria etc removed, de-ionised has had its ions removed so it supposedly takes ions from wherever it can to rebalance itself.
I use distilled water and ptnuke phn.
Distilled water has been boiled off and condensed, leaving most of the minerals and other rubbish behind. Deionied has been passed through a resin (if memory serves sodium is involved), most of the ions and general rubbish adhere to the resin. Distilled is more expensive.
For our purposes it doesn't matter a great deal, once opened CO2 dissolves into it, and once introduced to a watercooling loop a small amount of copper dissolves into it as well.
The rate at which distilled, or deionised, water will attack copper is negligible.