What do you call a receptacle for a DVD or CD?

The black, polypropylene DVD cases are called, well, "DVD cases." Sometimes, they are also called "Amaray cases" because Amaray was the first manufacturer.

The clear, polystyrene CD Case is called either a "CD Case" or a "jewel case." The term "jewel case" is attributed to the packaging designer Peter Doodson, a Dutch designer, who worked for Philips.