The difference is basically that of design. Coffins are the traditional shaped box associated with funerals and are tapered at the head and foot but wider at the shoulders and with a lid which usually lifts off completely. Caskets are rectangular in shape and usually have a hinged lid.
Coffins and caskets can be made of particleboard (chipboard), timber (including cedar, mahogany, pine and oak) or metal. The lining is made of materials ranging from calico, nylon to hand-ruched satin.