Bees often make lots of cups which are never used. Queen cups sometimes get developed into queen cells. Once the bees decide to swarm or superscede then one, or more, of the cups are laid in by the queen and the larvae fed royal jelly. If you find a cup with royal jelly in it then the bees are intent on producing a new queen. Once this process starts the cup is extended in length and width to produce a queen cell.
I think the terminology of cup and cell pretty much describe their appearance. The cell holds the queen until she is ready to emerge.
A cell is a compartment where the larva is nurtured from egg to sealing and from which the healthy bee hopefully emerges when fully metamorphosed.
In the case of a queen the cells are either based on the queen cup which is a rather more leisurely way of development or the rather more urgent alternative of an emergency cell which will be a (hurried) extension of a worker cell.
The queen cell shown is the leisurely version, built away from the face of the comb, as an axtended queen cup (as shown also).