What is the difference between a sarcophagus and a coffin?

it is not different it is both the same but some have 4 sides and some have 6 sides.

Correction:

The above answer relates to the difference between coffin and casket.

A sarcophagus was originally (in ancient times) a burial receptacle made of stone.

In modern parlance, it is a highly luxurious coffin or casket (often made from cast bronze).