I think, fred, the proper distinction should be between somebody whom you invite to come to your house and somebody who turns up on your doorstep and comes in anyway, whether you agree to them doing so or not.
However, without getting too stroppy it was not I who first raised this distinction. I simply referred to somebody in one's house stealing the cutlery. I suggested that they, as guests, are abusing the householder's hospitality and likened that situation to that of immigrants committing serious offences. But sp sought to amend the analogy by suggesting they [immigrants] were more like paying guests or lodgers. On the face of it seems more appropriate since, as he correctly points out, most of them are working and paying their way. But I still imagine the landlord would be inclined to throw them out if he caught them assaulting his daughter however much he might need the rent.
But I think that's enough of analogies because they seem to create more questions than they answer!