Both are technically pure however distilled is just fine for your radiator. The thinking behind this is it has been boiled which leaves all minerals and particulate behind, the steam is condensed into water which is "pure" this will prevent deposits from the water be left behind in your coolant system. Deionized water is the same thing that is passed through an ion filter bed which then makes the water 100% pure so pure it will not boil at the standard 212 F and so pure you can spray it on electrical equipment and not be shocked it is how they was highpower lines to prevent hot spots from dirt build up. There is no need for the extra cost of DI water. Granted I am in the military but our DI water costs us about $10 per gallon.
Ira