The distinction is that in general “opening a box and extracting the value” makes no sense, as it's not a thing that can be done in general. If your box is a Ma

The distinction is that in general “opening a box and extracting the value” makes no sense, as it's not a thing that can be done in general. If your box is a Maybe, there might not be a value to extract. If it's a list, there might be zero or multiple values. It only ever makes sense to map over the contents of the box, replacing the values with their image under the map.