deionized water is water that has been run through a filtration device in order to remove impurities. Similarly, distilled water is water that has been evaporated to remove impurities. When the water evaporates, the water vapor leaves behind impurities, and the water vapor is collected and cooled, where it becomes liquid water once again. After it changes from vapor to liquid, it is minus the impurities. So, both cases are removing the impurities. I think distilled is a little better at purifying the water, especially if it is distilled multiple times.