Ship's time is the time the ship observes, which may not be the same as local time. For example, most cruises to the western Caribbean from Miami stay on eastern time, even though the time in Cozumel is an hour earlier. So when in Cozumel, the ship's time may be 0900 hours but it is 0800 locally.
Sometimes ships will change time as they enter a new time zone, but not always. This is why you need to read your daily Cruise Compass. If a time change is going to happen, they will post information about it. ALWAYS ensure you understand the time you need to follow before you leave the ship. Many people don't think about it and start believing they need to follow local time. Then the ship leaves because it's schedule was an hour different, and dumbfounded passengers are observed standing on an empty pier.