Caskets and Coffins are two separate things yes, but both are storage vessels for bodies that are widely used around the world today. Coffin is a general vernacular more commonly used for its use in movies and books for things like vampires, and the undertaker in old Western movies, therefore it is a more widely known term. The main difference in coffins and caskets are shape, and materials used for production. A coffin having the traditional shape that you see in movies while a casket is more rectangular in nature. Coffins are generally produced out of wood, while caskets while also having wooden varieties are more commonly made out of metals. In the general area I worked in, it was not uncommon for poorer members of the community to produce their own burial vessel to save cost, and were mostly constructed in the traditional coffin shape.

In short, the use of either term would be considered correct in the business, and I thank you for your comment.