Both. You made me a bit curious so I decided to look a little deeper and see that a lot of the appliance stores/chains have both "hot water heater" and "water heater" in their meta-tags. What I find interesting is they also have "tankless water heaters" as well. Have you guys seen heated floor systems? There you have a "boiler" heating the water instead of a "hot water heater/water heater" and it's stored in a circulation tank. My fridge has a water dispenser, but it's not called a "cold water dispenser." The water cooler at work has hot water.
Happens occasionally. I appreciate you taking the time out of your day to point it out--to no inconvenience, I hope.