For simple objects, it’s just a different way of saying the same thing. An object that is less dense than water will float because its volume displaces a volume of water that is heavier than it, because it is less dense. (Overall as a solid, even if not uniformly throughout it’s inside)
Boats can have extra bits plonked on top which adds weight without increasing watertight displacement, so the weight/displacement thing has more utility.
Sully’s plane floated long enough to get everyone off safely, that’s long enough. If you want it to float longer, get a seaplane, but even seaplanes leak.
I’m not as familiar with Boeing’s procedure, but Airbus have unique part numbers for each unique manufactured part, but not serial numbers. So you can confirm that the part came off a particular type of aircraft, but not a particular plane.