The choice of box styles available to make cardboard boxes is substantial. It helps to understand the different methods of manufacture because the different methods affect the cost and the lead times for making the boxes.
There are many ways cardboard boxes can be made and ways to categorise those methods.
One way is to group them into the way the machines make the boxes.
The most versatile and slowest is using a "Plotter Table" or "Sample Maker". From large sheets of board, on a table, a "head" moves around the table cutting and scoring the shape of the box. It does this one item at a time and each sheet has to be positioned manually. Very slow - thus very costly. They do not print. They can make all the box styles available.
The next group is the "case makers". These make a select range of box styles; but, these styles are most commonly used. To assemble these boxes you have to tape, glue or staple them to seal them. They all have 90 deg angle corners and straight edges.
Some types can make a wide variety of these styles but they usually produce only a few hundred boxes per hour. Wise's Boxes uses this type of machinery.
Others make fewer styles but run much faster, producing upwards of 15000 cartons per hour. These styles usually have the option of adding printing, using the flexographic method. This method is normally makes the cheapest box.
The last group are the "die cutters". The boxes are cut from a pre made "die forme", which is bolted onto the "die cutter". The "die forme" is a knife/score blade made in the exact shape of the box. This method allows for curved shapes and locking tabs in the box styles.
There are two types of "die cutters"; they are, "flat bed" and "rotary". "flat bed" is suited to smaller qantity runs of several hundred to a few thousand. They usually do not print and printing has to be done on a "case maker". The cost of the box is more expensive than the "rotary" method but the "die forme" is cheaper. I have included a picture of a "flat bed die forme" that makes a Spare Parts Tray.
"rotary" is suited to production runs in the thousands. The curved "die forme" is shaped to fit onto the cylinders of special high speed "case makers". These machines can also print at the same time. These machines can cost millions of dollars, so imagine how many 50c boxes have to be made to make a profit.
Sounds confusing? It is, and it gets worse because there are many different types of machines in each group.
So how does all this affect the end user of the box? From a lead time perspective, it could be delivery varies from 2-3 days to 3-6 weeks, see the blog post on lead times. From a cost perspective, the smaller the quantity ordered the more expensive the box is. The more complex the box design, the more expensive the box is. If you avoid "die cut" box styles you will get your box quicker, and at a lower cost.
"die formes" incur a one off tooling cost. Dies range from a few hundred dollars for "flat bed" dies to thousands of dollars for "rotary" dies.
Hope this generalisation I gave helps you in your box buying.