Both a Coffin or a Casket are words used to describe a container for burial or cremation.
The only real difference is the shape. A coffin gets wider at the shoulders and then thinner towards the feet. A Casket is a rectangular shape and is usually bulkier and heavier than a coffin.
Other differences include the materials used for construction. Caskets are usually constructed from metal or wood whereas Coffins are more varied and can be constructed from materials such as veneer or solid wood, cardboard, wicker, wool, bamboo etc.
A Casket for the deceased should not be confused with a cremated ashes Casket, which is used for burial or storage of cremated remains.