Reverse osmosis is the process of forcing tapwater through a membrane that allows only pure water molecules through to the product side, the waste is passed through the other side to drain, most RO units produce 1 gallon of RO water for every 3 - 5 gallons processed, so it is wasteful and something to be thought of when you are on a water meter.
DI water is water that has been passed through an anionic and cationic bed to remove all the impurities by adsorption and chemical bonding
Reverse Osmosis product water and DI water have 0 GH and 0 KH and can then be chemically altered to suit your tank requirements.
RO and DI water cannot be solely used to fill your tank as it is is sterile and will not sustain life, additives have to be added to make it suitable for fishkeeping, but it is nitrate, phosphate, and contaminant free
Dependent on your water conditions DI can be highly expensive, we live in Essex and 1 litre of DI resin lasted for approximately 60 litres before it was shown to be discharged ( resin changes colour )
We have a 100 gallon per day pumped RO and with the reef and the stingray/arowana we wouldnt be without it, but other people quite happily use dechlorinated tapwater with no real adverse effects.
At the end of the day you pays your money and makes your choice