Maybe he/she was referring to more detailed roles.
It all depends what site you're working on/with. If you're a webmaster of a personal site, then you're a web designer and content manager.
If you're responsible for a whole commercial site of a small company, then most probably you're a designer, content manager, database admin, and application programmer (depending on the site they want, of course). But I think for bigger companies, they usually have a team of webmasters with varied tasks and roles than to have just 1 webmaster to do everything.