Distilled Water is water that has many of its impurities removed by distillation. Deionised Water is water that has been filtered chemically to purify the water.
Distilled water tends to be more expensive than Deionised but much purer, Distilled water tends to be used by laboratories and in food processes deionised normally in machines that heat water to stop build up of chemical residues.
At County Battery Services Ltd deionised water is supplied in large quantities for topping up of batteries for fork lift trucks in general. It is also used in a number of manufacturing processes.
To distill heat it to steam (so it vaporises) then cool the steam so that it condenses and collect the liquid. Because the water will vaporise before any of the impurities it effectively removes to impurities from the water. To make really pure water this process can be repeated.