It depends on what they actually do. If it's more graphical/architectural then they're a Web Designer. But if the job is more functional/programming, then they're a Web Developer. A big company will segment that out a lot further, from illustrators to application developers, to database engineers and so on. But smaller organizations might just have one person. If that's the case then webmaster still applies. That being said, if I was hiring a person to run my web site(s) I'd advertise for a Web Developer, because it sounds more professional.