Conversation so far:
what is the box called when you die
A coffin is a funerary box used for viewing or keeping a corpse, either for burial or cremation.
A casket is the same as a coffin?
Coffins are tapered at the head and foot and are wide at the shoulders while caskets are rectangular in shape and are usually constructed better.

Question: Do both boxes go on display?
Self-contained rewrite: Do both caskets and coffins go on display?