For the boxes, the far right one w/two bands opens at the top. The one on left is a version that opens on the end.
Both of the boxes in the kit are end opening. Neither of them has hinges or latches for the lid. Top opening boxes have cleats on the lid.
The three pack round containers (wood box and tootsie rolls) I believe were used as airborne containers since they were lighter than the wooden boxes.
The difference between the crated cloverleaf bundle and wooden box was less than 3 lbs/rnd. An individual triple pack was over 50 lbs (40%) heavier than a two round box, however. The airborne forces mainly used 75mm howitzers I believe, but that's straying from the point.
The wooden crating on the cloverleaf bundles of fiber tubes was used for overseas shipment. The bundles were shipped domestically without crating and the crating was usually removed at the ammunition supply points before issue to the batteries.
My article (referenced above) is worth reading if you want to learn about the subject.