Only one aircraft is actually allowed to depart/land on a given runway at any one point in time.
You can have clearance to land after the aircraft in front has landed or departed, but broadly two civilian aircraft occupying the same runway is a no-no if either are taking off or landing. Seaplanes is another matter entirely, and of course there are dozens of exceptions.
You can have multiple aircraft cleared for a departure or arrival or approach - but note that this is not a clearance to take off or land.
I've been given clearances to land roughly 5 seconds before my wheel touch and my hands were just about to shove power in to go around. I've been told to go around after my wheels are on the runway too.
We usually know what ATC is doing or waiting for and we can anticipate those calls.
I don't think the US is different from the RoW in that manner - they all need to conform to the ICAO regulations - otherwise we'd have chaos with US pilots navigating China or vice versa.
Me: FAA (US) & CASA (AU) PPL w/MEA + IR.