In practice though, there really are three discreet focal areas, at least in my experience: art, design, and engineering. There is often some overlap between; technical artists will be able to do some coding and shader work and may have an eye for design; versatile designers will be able to do some coding or art, and some competent coders will be capable of working in the other disciplines (although in my experience these people are rare, coders tend to be math geeks who happen to be in games because it's somewhat more fun than coding java applets or databases or whatever).
Of course there is usually an army of other people required by the business, HR, Marketing, QA, management and so forth. but that's not why we're here is it