Planted Tank Guru
Join Date: Jan 2010
Location: Contra Costa CA
Deionized water has the cations and anions (the charged particles) removed, but the other things in the water that are not charged are not removed.
Distilled water is water that has been evaporated in one container, the vapor lead to another container and allowed to re-condense. This process removes almost everything in the water, leaving a residue in the original container.
Most TDS meters are measuring the charged particles in the water, and then equating the results to salt. If there was sodium chloride only dissolved in pure water it would separate into charged particles (Cl- and Na+), and result in a certain reading from the TDS meter. Since the TDS meter does not read non-charged particles there may actually still be 'stuff' in deionized water. It just does not show.
Both distilled and reverse osmosis systems do remove more stuff, both ionized and not ionized things. These are usually closer to pure water, though the quality of the equipment plays a big part in this.
Many of the chemicals in tap water are charged particles, so you are getting a purer product than comes out of the tap (or well, or river...) with any of these procedures.