Rigid boxes is also known as set up boxes. These kinds of boxes consists of two parts lid and base. With respect to lid classification different types are available e.g telescope lid it includes(full, partial telescope, Tray with Sleeve, neck box)  Hinged Lids include (Clamshell Style, Flip Top or Cigar Box).

Credit: https://www.thecustomboxes.com/rigid-boxes/