Here what I know about the difference between them.
RO-Reverse Osmosis is basic filter water that remove chlorine and dirty water through several carbon filters. It usually best process at least two types of microns such as 10 and 5m microns. However, RO leaves mineral trace, which you can taste.
DI-Deionization filter the purest water, leaving no minerals, trace such measure in total dissolve substance. It is filter through a special membrane that collects every substance.
That's what I know about RO and DI.