Deionized water is mineral-free. Distilled water is not (low mineral).
Deionized water and distilled water are both types of high purity water. They vary in a make-up however due to different production methods.
Deionized water (or DI water) is water that has been treated to remove all ions (i.e., dissolved mineral salts). This is usually done by running tap, spring or distilled water through an electrically charged resin.
Distilled water in contrast, is water that has been boiled to steam, and then re-condensed back to water in a secondary vessel. This method will remove most impurities and minerals, but not all (some can vaporize along with the water).
Note: both of these water types are suitable for Sentia acetic acid dilutions but ONLY IF reagent grade. Most wine laboratory supply stores will stock reagent grade water. Please do not buy your water from the supermarket.