How does an immersion heater for a bathtub work? We don't have them in America.?

I have been reading a lot of Katie Fforde books and it seems all her character's bathtubs have immersion heaters. The only immersion heater I am familar with is a little coil that is plugged in and stuck in a mug of water to heat it up. I can't imagine that is how it works for a bathtub. On a side note, I find it interesting that in the English books I read, the characters only take showers if that is all that is available. In America, only kids take baths on a regular basis - adults take showers. Is the plumbing that different or is it just a cultural thing?