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Quote:
semi-detached home is owned, not rented

No distinction is made

Perhaps it'd be more accurate to say that the two semi-detached houses can be independently owned (and usually are), as opposed to a building of two flats, where the flats will be leased or rented from the building owner, because it doesn't make sense to own one flat outright. You can't exactly say "I'm demolishing my ground-floor flat, hope that's OK with you people upstairs", whereas it's perfectly possible to demolish one of a pair of semi-detached houses.

It sounds as if "duplex" doesn't capture the important distinction of whether the two dwellings are vertically or horizontally duplexed; Wikipedia says that semi-detached is the official term even in US English, with "duplex" being more colloquial, but that sort of local dialect precision is exactly what Wikipedia is least good at.

Peter