What's the difference between 'lead', 'cable' and 'wire'?
And which of these words is more commonly used for, say, household appliances or office equipment?
"Cable" is thicker than "wire", however that doesn't really explain when to use each of these. Also, in American English, for household appliances or office equipment we use "cord" for some things and "cable for others", and occasionally "line" or "wire": power cord, ethernet cable, printer cable, telephone wire (or in a different context, "telephone line").
"Lead" is not common American English. I'm not sure if it's used more in Britain, or it may be used commonly in certain professions. More often in the U.S. you'll hear "wire", as in, "No wonder it doesn't work; the wire's detached."
As a related note: A recent movie "Man on a Wire" documents the amazing feat of French daredevil Philippe Petit who is (and will always be) the only man to walk between the Twin Towers of the World Trade Center in New York City. If you watch the film, obviously he uses a cable to walk on, because it's very thick and sturdy -- but he's called a "wire-walker" because that makes it sound like he's walking on something very thin and easily broken.
The first thing that comes to my mind with lead is that it's a different term for a leash, like that you'd use to walk a dog.
Cable is either A) thick and often reinforced or otherwise protected from harsh elements - e.g. designed for outside or in-wall use, and/or B) consists of multiple thinner wires. So we say phone cable, network cable, coax cable as opposed to wire.
Wire is thin and not reinforced or protected in the same way as cable.
Thin cables with 2 wires only are often called wires, such as phone wire or speaker wire.
Wire - a single strand of ductile metal, extruded from a die.
Cable - multiple wires or strands bound together for better mechanical / electrical properties than a single wire of similar thickness.
Line or Lead (elect.) - a wire or cable used for electrical transmission.
Cord (elect.) - insulated conductor used power to an electrical appliance
these can be interchangeable.