The difference is not intent but use. This is the same with real estate: if I own a building to live in it, that's personal property, but if I own a building to rent it out or run a business in it then it becomes private property.
Whether an actual communist society would organise housing like this isn't clear. No-one would reasonably consider Marx's writings to offer a societal blueprint, just principles from which actual details would be worked out through collective processes.
That it's never actually worked out like that suggests there's been something missing when this has been tried, but this doesn't correspond to proof that the principles themselves are wrong.