They are called storeys. I wonder if its because things would be stored in the space below the roof, above the main floor. So perhaps any floor above a ground floor became known as a storey? just a guess!!
the idea seems to have been that in a church, one 'storey' would have a row of stained-glass windows that told a story. This sounds implausible to me, but it's what the etymologists say. In which case the American spelling is more logical than ours.
Thanks everybody - windows telling a story seems to be the popular conception, trawling around, but Katy's seems more logical. Should have contacted 'Balderdash and Piffle' !