Diesel generators simply use less fuel if there is less load than the maximum.
Note that generators need to run at constant rpm to provide the correct ac frequency. Your car has gears so that it can run at lower rpm at low loads and so you won't see the same effect.
Yes it was a tanker. The bigger the ship doesn’t mean it has more people or more power generation like a cruise ship. A tanker has a crew of 4 plus captain, maybe?