Cubanboy has already provided the basic answer. Each of the words can be used in several senses. "audition" meaning "the ability to hear" is a technical term little used by non-specialists (although it is, of course, related to more common words e.g. audio, auditorium, etc.). "casting" can also refer to fishing ("fly-casting") or to a step in the process of creating a statue, metal object, etc.
In the world of theater/movies "casting call" and "audition" are used interchangeably. In this same world "casting" (without "call") is used to designate the overall process of selection (which may involve several "casting calls"/"auditions"). Thus, for example, one might say "They will begin casting the film in April and hope to start production in June.
P.S. I suspect (but haven't bothered to consult the OED) that the theatrical meaning stems from the statue-making process since we say "He was cast in the role of Hamlet."
