That's interesting, and I don't doubt that you have seen a system like that, but it sounds more like what could be expected in an industrial setting with 3-phas

That's interesting, and I don't doubt that you have seen a system like that, but it sounds more like what could be expected in an industrial setting with 3-phase power. The few houses that I was involved in wiring of in the states were definitely "split phase" systems, which work like the GP describes. In those, three current-carrying wires come from the transformer - two ends and a centre tap from one winding. Those are wired in the breaker box so that the house has two circuits that are 180* off from each other, giving 110V on either circuit, or 220V between the two "hot" legs. There's a better description at https://en.wikipedia.org/wiki/Split-phase_electric_power https://en.wikipedia.org/wiki/Split-phase_electric_power.