The Hot Water Heater also is a Cold Water Heater, and maybe just a Water Heater. But after the Hot Water Heater heats up the Cold Water, the Hot Water Heater keeps the Hot Water Hot. Thus, the term "Hot Water Heater". :). You see, most of the time, if left on, the unit will be heating Hot Water (this also implies that there is a Thermostat involved). Only when first powered up will it heat Cold Water.
Just another point of view......
Ken Powers
SM2K 262