That's a good question ... I've seen two models, one where if you have access to a separate bathroom and stay in that area and not mingle with the household. The other model is that the traveler needs to stay somewhere with no others (except those travelling with them). This does not necessarily mean Hotel Quarantine in the sense that we know it. It might be your own hotel booking and arrangements, or airbnb or the like.
As an example of what is happening elsewhere - Singapore has a 7 day home quarantine requirement for those returning from Australia, which we will be doing next month. At one point it was looking as if for various reasons, I would be returning 2-3 weeks earlier than my partner (not happening thankfully). Singapore only allows people to do home quarantine with others who were travelling with you on same itinerary, and no one else in the household. We had already decided that if I came back first, when my partner returned he would quarantine at home and I would find somewhere to stay for the week (rather than the other way around). Much easier for the "quarantinee" to be stuck in home with full facilities, and the "free" person to be in a hotel, as they are not stuck in the hotel room 24/7, and therefore can use the hotel as a base and come and go, dine out etc.