Closed box bending
The story with boxes bending is one of the main theories to study the principles of bending, work of press brake tools and imagine the positions and steps in your head. Don't know exactly the number but bending of boxes also is the main task for press brake - all electrical cases mainly are boxes. The second story could be doors with the same concept like closed boxes but with other dimensions.

What is the story and main differences about box bending?

At first "box" is the application which require sectioned tooling. Because of 4 sides it means that you can't use the tool of any length like any opened bend or profile. You will have lateral sides and it means that you need the length of bending punch exactly the same as the length of bending, not more (because you can't of lateral sides) and not less (because you will have not completed deformation at the missed areas). Sectioned press brake tools mainly not are for boxes only but if your box length is outside of standard length of the solid punch it means 100% that you need sectioned tool. And if you have the length which is not corresponded to the sections summary probably you need also the punch cuts with special length. It also means that if your required length could not be divided for 10 mm (because 10 mm is the smallest cutting piece in sectioned tool set) you also have to made the special length piece.
Moreover, probably, if the production of one part is big but you have the necessity to replace the punches on press brake, you should think to have your length in minimum quantity of pieces instead of installation of small sectioned tools.

The second story - if you have closed box even sectioned press brake tools are not enough but you need to have horns. Horn help is required to bend if upper shelf of box will make the collision with the punch (which is normal for closed box). Horns are only solution and equal to the possible width of shelf you can obtain. The bigger shelf require special horns development. Horns could be also really unique if the bending will be of box or panel different than 90 degrees angles. Horns deepness in standard tools is not very big - usually 20-25 mm which is enough for typical boxes. The configuration of closed box and upper shelf is necessary to make the proper welding and probably use some connection points to attach the box so the standard horn is enough.

So mainly bending of box request 2 questions - how to bend (sectioned tools + horns for last internal bends) and how to extract. Extraction means that after the bending you can't just make the return move - it is not enough to remove the horns. Normally parts usually are extracted with diagonal repositioning and even this reposition is not enough - it is possible to obtain movable horns. The additional difficulties could be when the part is big and heavy - it is quite hard to positioning it by operator for extraction so these applications in practice are mainly the subject for automatic and robotization.