DeIonized water is usually Reverse Osmosis water that goes through one more filter to remove ions (duh).
Its used fairly common in many industries, for the same reason we all use RO... tap water has 'who knows what' in it.
Distilled is a whole different process, involving boiling, where RO and DI are usually just filters. I'm not going to sink into the argument if distilled is 'better' or 'worse' than RO/DI. You can get distilled at Wally World or the grocery store, and its usually about the same as RO/DI, but buying RO/DI gives you an excuse to window shop at the LFS, so you gotta go that route.
BPN, just make sure your company changes their filters religiously. You'll notice problems in the tank before they will (depending on what they're using it for, of course).