Hi Guys,
Amy, of course it's a GREAT question!
"Cast" refers to the way a gold part is made.
A model is made, and it can be re-used to make hundreds of rings. If it's a one piece model, any single metal can be used.
As snooper mentioned, a split shank halo model we love IS made from one part ( shown below with a few special yellow gold parts we made by hand)- and can be ordered in any color of gold ( including pink)- or platinum.

The Hal1 style- as shown below is made from multiple parts- that's how we can do the pink gold halo.....

"Custom Made" rings have parts that are also cast- but in these cases, we've designed one of a kind models around the diamonds- or hand made parts in some cases.
Another method of making parts for jewelry is called "Die Struck"- a much heavier method involves stamping gold and platinum parts.
Since the dies can cost many thousands of dollars ( as opposed to a few hundred for a model for a casting) "Die Struck" parts are not practical for ring styles which need to have multiple versions in terms of size, and stone shape. The split shank ring shown above comes in at least 25 different models of shapes and sizes.
We use shanks and a few other parts that are die struck.