Many laser machines only have nozzle that blow air from top to bottom. When doing engraving, the debris could be blown back to the engraved area, and it is hard to clean.
When air is blown from the regular nozzle, the white base material has green debris. With the air assist blown from the side, the engraved area is clean as shown. Sometimes the engraving direction is from rear to front. If you are using Lightburn, the engraving direction can be changed so the smoke can be blown towards the unengraved area.
Some laser machines are mainly for engraving, so they do not have nozzle for cutting. One way to have strong air flow is to direct the air down towards the cutting area. Although it is not as good as blowing air along the laser beam, it is better than the original weak air flow came with the machine. Some small machines with large nozzle hole also suffer from the weak air flow problem.