Cutting of folding cardboard is possible. However, you need to consider a light discolouration of the edges. In the application, this is generally accepted, as lasers will be used for intricate short run designs.
Creasing of folding cardboard is also achievable, by scoring/burning away the top layer of material. Mechanical creasing is always preferred as scoring cardboard weakens the crease significantly.
Marking/engraving is easy to achieve.
Cutting of corrugated cardboard is similar to cutting folding cardboard. However, the discolouration can be more visible since the smoke can run through the fluting. Thin corrugated board (E-flute e.g.) would be easier to laser cut than thicker multi-walled cardboards. Creasing, on the other hand, is better done mechanically than by using a laser. Then, part of the material would need to be lasered away to achieve a crease. This is not recommended as carbon and discolouration will always be present.
You could crease by lasering a perforation line, but this also would be weakening the crease.
Marking or engraving of corrugated cardboard is a more common application.
Lasers are more commonly used to create a die. This is due to the fact with CNC machines you are limited to the thickness of the router bit, while on a laser the spot point is a lot smaller (0.1 to 0.25 mm)
Laser machines to cut folding cardboards are mainly used for short-run intricate designs, especially for greeting cards. It's a lot less or not used for corrugated cardboard. Mainly because of the discolouration of the material after lasering.
Within the packaging industry, lasers are mainly used for die-making.