USPS, as an incentive to use its Priority Mail services, offers free Priority Mail branded boxes. There are three kinds of Priority boxes with different associated pricing schemes:
Regular - priced by weight and distance (Measured by “Zone” with Zone 1 being local, Zone 8 cross-country, and Zone 9 a very distant location like certain US territories)
Flat - same price no matter the weight or distance
Regional (Discontinued) - priced by distance and as if a fixed weight
You can also provide your own, “brown” boxes to ship Priority mail, but only at the regular Priority rate. In order to get Flat or Regional rates, you must use the branded boxes provided by USPS for the specific special rate.
Effective January 22, 2023, Regional Rate Box pricing has been discontinued. Remaining boxes can be used for shipping at weight-and-rate packages.