Dehumidifier water is not distilled. Stanford Magazine says that water from a dehumidifier still contains biological contaminants in addition to metallic residue, whereas distilled water contains neither.
The way a dehumidifier works is not that different from actual distillation, as both have final results of evaporated and subsequently condensed water. However, the heavy metals in the dehumidifier are always present, and any unsterilized environment (such as the tank) serves as an open environment for microbes. Water collected from a dehumidifier is known as "gray water." This kind of water is not recommended for human or animal consumption, but it is deemed safe for other uses, such as watering plants.