Rather than comparing the two processes in the abstract, it is more useful to go through the jobs people actually have. In several of them the two are interchangeable, in several one is clearly preferred, and in one of them using the wrong one causes real problems. The deciding factor is usually whether anything uncharged has to be removed as well.
Car washing and window cleaning: deionized
This is DI's home ground. What matters is that the water leaves nothing behind as it dries, and resin achieves that at full flow with no waiting and no power. Distilled water would work equally well chemically and is completely impractical, since you would need to produce or buy volume that a still cannot deliver. Use the DI stage for the final rinse only, after washing with ordinary water, which multiplies cartridge life considerably on hard supplies.
Aquariums: usually deionized, often behind a membrane
Aquarium keepers want a blank base to build known water chemistry on, and DI delivers it at usable flow, which is why reverse osmosis followed by deionization is the standard arrangement in reef keeping. Distilled water is used by some smaller setups and is slower and more expensive per volume. Whichever is used, the water is remineralized deliberately for the species kept rather than used bare, since fish and invertebrates need specific chemistry rather than an absence of it.
Steam irons, humidifiers and batteries: distilled
These are the applications where distilled water is what manufacturers specify, and there is a good reason beyond mineral content: distillation also leaves organisms and non volatile organic material behind, while deionization removes only charged species. For a humidifier or a CPAP machine, which turn water into something you breathe, that difference matters. Battery topping up specifies distilled water for the same conservatism. Follow the appliance manufacturer rather than substituting.
Laboratory work and drinking
Laboratories use both, and which is required depends on the analysis: DI for work sensitive to ions, distilled or higher grades where organics matter. For drinking, neither is the intended product. Both taste flat, since the USGS describes hardness as dissolved calcium and magnesium and both remove them, and DI water from a technical unit should not be drunk at all because nothing in that system was designed for safety. Our softener guide covers hardness across a household.
Questions people ask about deionized vs distilled water
Which should I use for washing a car?
Deionized, used for the final rinse only. It delivers at full flow with no power, which distillation cannot.
Which for an aquarium?
Usually deionized behind a reverse osmosis membrane, then remineralized deliberately for the species kept.
Which for a steam iron or humidifier?
Distilled, which manufacturers specify, partly because it leaves organisms and non volatile organics behind as well as minerals.
Can I substitute one for the other?
Often, but not where organisms or organics matter, such as humidifiers and CPAP machines. Follow the appliance manufacturer.