A cast is the group of actors who make up a film or stage play. And the act of being chosen for the part? Well, they were cast by the director. That's showbiz for you.
Cast also refers to various types of actions a person can take: if you throw out a fishing line in a particular way, you are said to cast it; if you fancy your chances in Vegas, you cast the dice at the craps table. And if you break a limb and they bandage it up in solid plaster for your friends to write all over? That, too, is a cast.