Yeah, that's not what's generally meant. That's a point-of-use (or something like that) heater. Personally, I don't like the concept of electricity heating the water right at the point I'm using it. Seems too easy for it to ground itself through me.

Anyway, a tankless heater is basically one that replaces a "normal" (in the US) hot water heater and automatically switches on a gas burner when it detects that a hot faucet has been turned on to heat the water in the pipe as it comes from the water supply without storing any of it. People complain that they don't produce enough hot water to feed more than one thing at once, like a shower and the dishwasher, but other people say that they work just fine. There is certainly some benefit to not having to keep a few dozen gallons of water heated in a tub with immersion heaters all the time.

I'm sure that part of my problem is my low water pressure, which means that it takes a good while to get all of that cold water out of the pipes. But a refit recirc system is cheaper than hiring a plumber to fix the water pressure. And its benefits wouldn't go away when I finally do get the pressure fixed.