The main difference is quality of this solvent. In some applications, you have to use a higher quality : for example for injection or ocular treatment, you have to use sterile water. Thus you have also some tests to prove the quality.
Thank you everyone for your nice and informative answer. This three types of water are used in laboratory for research purpose. Basic differences are:
Distilled water has been boiled so that it evaporates and then re-condensed, leaving most impurities behind. It is a process that kills off additional contaminants such as lead, heavy metals, salts and chemicals. Boiling the water for 20 minutes at 250 degrees Fahrenheit kills off any bacteria or microorganisms.
Deionized water that has been treated to remove all ions typically, that means all of the dissolved mineral salts.
Distilled water is more pure than Deionized water.
Sterile water: The microorganisms are destroyed by heat above the boiling point, or 212 degrees Fahrenheit.