This is a common point of confusion in lab management. Distillation involves boiling water to create steam and then condensing it back into liquid. This process is effective at removing bacteria, pyrogens, and many solids, but it is slow, consumes a lot of energy, and can actually concentrate certain volatile contaminants.
Deionization, on the other hand, does not remove organic compounds, viruses, or bacteria unless paired with pre-filters or UV lights. However, it is incredibly efficient at removing ionic impurities, producing high-resistivity water very quickly. Most modern labs use a combination of both (or Reverse Osmosis followed by Deionization) to achieve the purest water, rather than relying on one single method.