DI water is de-ionized water that has had all (read that as most) of the ions removed via ion exchange resin. The process uses cationic exchange media to remove cations (calcium, sodium, magnesium, etc) and exchange those with hydrogen ions (H+). It then send the water to anion exchange media beds to remove anions like chloride, sulfates, nitrates etc, and replaces with hydroxide (OH-). The result is an exchange of mineral ions with H+ and OH- to form H2O. The process is not 100% efficient, so the purity of the DI water is based on a lot of things. Usually 99.95% removal

Distilled water tries to accomplish the same thing using heat to distill off the pure water while leaving the salts behind. Based on the set up of the still and the level of possible distillable organics, the water will be essentially pure. It will be for all practical purposes, be equal to DI water.

Reverse Osmosis (RO) water uses a selective membrane to remove ions by utilizing overcoming the osmotic pressure of the water and pressuring the water through a membrane with pore size at the molecular size. The process is 99% efficient, so approximately 1% of the minerals still remain in the RO treated water. The home RO units you sometimes see used on kitchen faucets of under sinks do not produce the pressure needed to complete the process, so they are usually less than 80% removal of ions.

Soft water uses ion exchange as well, but only uses the cation exchange resin and uses sodium based resin instead of hydrogen form resin. Calcium and magnesium are exchanged with sodium (or potassium if you use KCL rather than NaCL where you might be on a low sodium diet).

The DO meter will be fine using distilled water bought in 1 gallon bottles at the grocery store.

Hope that helps.

Mike