Overnight means…overnight.
What is all this ambiguity we seem to have about simple words. In any other context where someone would say “I’m going to stay overnight in London on my way to Budapest,” or “I have an overnight flight,” we know exactly what that means. It’s overnight. From tonight to tomorrow. This isn’t hard, people.
An overnight for me has always meant the guy stays, sleeps with me, and we part ways the next day. It’s really straightforward.