And NEVER de-ionized water... only distilled water. The former may leach metals from your system, I'm told.
Distilling water leaves most ions behind since they evaporate at a higher temperature than the water does. But, not all -- some organic contaminants evaporate *first*, so they would remain in distilled water (e.g. ethanol) Indeed, this is why you use a still to make booze from a mash or even a wine (the ethanol evaporates first); when the temperature rises to near 212F you've got all the booze out and now you're distilling the water.
True pure water has zero TDS in it (dissolved solids) and zero disassociated ions (e.g. NaCl) in it. It has extremely low conductivity (water actually has very low conductivity; it's the ions that make it conductive.) And yes, both deionized and distilled water are extremely
aggressive -- pure water is an extraordinary solvent, which is why you never, ever use it "neat" as a coolant -- anywhere. Even places where very pure coolants (e.g. a nuclear plant) use water don't run pure water -- there are additives and buffers intentionally added and the chemistry is very, very carefully balanced and monitored to account for this.
There are certain specific exceptions where you want to run "pure" water in an engine because water has more specific heat capacity than glycol (for example) and thus it will transport more heat -- about 10% more than a 50/50 glycol/water mixture. If you have a marginal cooling system in something you may want or need to do this to prevent overheating. IF this is necessary, AND you have no need for freeze protection, there are additive packages (e.g. Fleetguard) that can be mixed with pure deionized/distilled water to prevent corrosion and make doing so safe. One specific place where this is common and necessary is with older 2-stroke Detroit Diesels in marine service where the company that marinized the engines cranked up the output beyond what the factory cooling system was designed for and could handle but didn't replace the heat exchanger with one that has higher capacity -- and you use your boat in a place where hard-freeze temperatures are NEVER encountered.
Distilled water, in most cases, is usually more
pure than deionized, especially if the distilled water was filtered first and/or it was double or triple-distilled. In lab applications where even tiny impurity concentrations can cause problems this can matter. For use in a cooling system either is fine but distilled is cheap enough in the quantity required (about a buck a gallon, much cheaper than the glycol and additive mixture you use it with) and available at nearly any grocery store, so there's no reason to use anything else.