Distillation removes all inorganics and destroys or removes many organics. Particulate matter is left behind. From a volume distiller DW is easy to make and can be quite inexpensive.
Deionized water is made by running water through a mixed bed ion exchange resin which can be quite slow and quite expensive when compared to distillation.
The resin, once used, must be either discarded or regenerated, but a still can be kept operational for weeks or months at a time. They do need cleaning every once in a while to remove mineral scale.
For high end use, DI DW is used for ultimate purity. We at EK only used this for emulsion making in the most critical instances. DW was used to mix some solutions and tap water was used for things that were not sensitive to calcium or heavy metals.