Rigid boxes, or setup boxes, are a high-end variety of paper boxes. They're stronger and more durable than folding cartons. They have life beyond their initial use as keepsakes for jewelry, trinkets, photographs, etc.
Pictured: magnetic lid rigid box for American Express.
Bottega Louie rigid cuff box with heart shaped diecut paper insert.
Seasonal Bottega Louie macaron box
Telescope Box for RFC