The difference is a man’s home is his castle. This make a big difference when it comes to arresting and evicting. Most states probably have very specific laws about eviction (I know Canadian provinces do). The police have to decide who’s telling the truth. It could be a landlord who wants to give his tenants the hoof and lies about their lease. It could be real break and enter squatters. They may have had an arrangement with the previous owner… etc. It’s probably a lot easier to arrest the guy who pried open your door and is snoozing on your couch in a house full of your possessions, than the usual squatter scenario where someone finds there are people who have been living in his property, not his primary residence, for a month or six and now he wants them out.
Cars or babies are easy. A car has title. In the event of a dispute, they police tow the car and the person with the papers and ID can retrieve it (for a fee). In the event of a custody dispute, they call child and family services, who look over who has custody. You can’t tow a house, except in the really low-rent districts.
But in both cases, theft or kidnap charges, and certainly conviction, are not guaranteed if the person claims they were permitted to take said item. People rent property to strangers all the time. Just because the rent is not paid does not make that theft re trespassing - it falls to the Landlord-tenant laws. People don’t usually lend their car or child to someone they have never met. The person caught in those circumstances likely has some ‘splainin’ to do. OTOH, if an irate girlfriend calls the cops and claims her boyfriend stole her car, and he says she lent it for the afternoon, odds are that would be an interesting case, certainly no slam-dunk; but if he’s had it for 5 weeks and is two states away, more likely it will fall on him to explain.
Cops make decisions but they have to be careful that they are certain the facts are straight. Real estate isn’t going anywhere. Let the judge decide.
IIRC “notorious” means the occupation has to be obvious and well known, not hidden; so that if the owner knew and cared about his property, he would easily have known. No sneaking in the back door and leaving the windows boarded - the lights are on at night and you come and go in broad daylight like you own the place and everyone can see this.
IIRC in several states and provinces like in Ontario, any title disputes like adverse possession are replaced by the computerized title registry and that is the sole and authoritative reference for titles. The only exception is if fraud is committed against the registry.