As I understand the term, British garden sheds are small workshops almost that a person can enter and walk around in standing fully erect and that he will do part of the work in. They have windows for light and workbenches, as well as shelving, etc for storing tools, chemicals, pots, etc. In the US and especially at present, the term more commonly refers to a small storage shed, maybe 8 ft x 4 ft, in which the gardening tools and sacks of whatever (fertilizer, potting soils, bug sprays, etc) are stored. They can now be bought as a sheet-metal shell with a single doorway (and two sliding doors) and no window. They stand at about a man's height or a little shorter, so anyone entering it would not be able to stand erect, but rather would need to stoop over. Nobody would want to go in there and work for any sizable length of time. And for whatever reason, it is these storage sheds that HOAs ban (I think they tend to receive no maintenance and end up rusting away and looking terrible which would lower property value, plus vermin tend to like to live in them). The American equivalent would be the garage or the basement, where the man has set up a workbench and where he keeps his tools and works on small repair projects. Usually, the man needs to install his own workbench and many home-improvement stores here will sell cabinetry for that purpose. In my new place (townhome-style condominium), it appears that the builder had gone ahead and installed cabinets and a workbench in the garage.