Candy box styles include:
The Loose Wrap lid with base. The base has a paper securely laminated to the chip board. The lid , however, is fully wrapped but it is glued only on the part of the wrap that turns inside the lid. The wrap is folded neatly over the frame of the lid to give a softer "blousey" look.
The Extension Edge base with lid. The base has a flat extension that slightly protrudes away from the side and end panels. The lid is full telescoping. When closed rests on the "extension" of the base.
What ever styles you choose, what ever your brand requires will be accomplished in a rigid paper box.