One airport under two names
Amsterdam Airport Schiphol is the full name on the signs; tickets say Amsterdam, locals say Schiphol, and all three mean one airport and the same service.
Tickets, booking sites and departure boards abroad tend to say simply Amsterdam. Inside the terminal the signs read Amsterdam Airport Schiphol. Dutch speakers shorten it to Schiphol, said roughly as skip-hol, and use the word for the airport and for the area around it. A newcomer can meet all three versions in the first hour and wonder whether they are the same place. They are.
What the name tells you
For a booking, the useful point is that Schiphol is not the city. It lies well outside the centre, joined to it by train, taxi and bus. A room at the airport and a room by the canals are handled differently here, not because one costs more but because the timing works in a different way. City rooms have a fixed arrival window; airport rooms have a journey time agreed first.
The surrounding areas
Schiphol-Rijk and Schiphol-Oost are business districts attached to the airport, each with its own hotels, and both belong to the airport hotel cluster. Writing the hotel's full address in the first message avoids any confusion about which of them you are in.
Using either word
You do not need to know which name to use when you write. Amsterdam Airport, Schiphol, the airport: any of them is understood, and the first visit page walks through the rest.