Language
In the USA folks use both phrases of "water heater" and "hot water heater" too.
Both phrases are in legal code books used in building houses, and literature, and markings on actual water heaters too.
Usage of both "ways" is older than any person alive, it goes back to steam boilers.
Todays 2009 International Residential Building code under chapter 20 in Boilers uses the phrase "hot water boiler" too, maybe to stress the difference where "steam boiler" is used.
Many folks say "hot water heater" since the water heater makes hot water. "hot" may not be really required, but I have never until this board heard anybody say mention that it is odd!
Folks in the USA too often say "lawn mower" too; and use the term "mower" too.
Thus yesterday a customer of mine said : "I will be back in a few hours, I need to take my lawn mower to my girlfriends house". If I told him that "lawn" was redundant he would think I was a nut.
In the USA folks can have water heaters for a pool too. Thus the added term "hot" often means it is the hot piping's supply for inside showers and sinks, not the pool.
ON house plans "WH" with a circle around the WH is often used.
SOME real old folks call our tanked hot

water heaters "boilers" too; even if wrongly they never boil water st all.
If one worked at Home Depot or Lowes building supply stores as an employee and tried to correct customers not to use the added "hot" in front of "water heaters" one would be warned at first, then if done again fired as one who drives off customers with silly correctness.