There are two categories into which purified water can be classified:

Distilled:

Distillation differs from all other forms of water purification in that the water is removed from the impurities rather than the impurities from the water. Distillation has the broadest capabilities of any single form of water purification. Distillation will effectively remove all ionized solids, all organics with a boiling point greater than water, all bacteria and with the addition of the special baffle, all pyrogens. Note that ionized gases and certain low boiling point organics were not mentioned. These impurities may not be effectively removed by distillation.

Deionized:

Deionization(Demineralization) removes the most prominent of the contaminants found in water, ionized particles and gases. Ionized impurities are removed based on their respective charges as cations(positive) or anions(negative). Purity level is monitored through electrical conductance.

Generally, distilled water is more often used in biology labs and deionized water is suitable for most chemistry applications.