Someone can be talented at both, expert in both and innovator in both. The real talent comes in doing them at the same time, within the same project and timelines. The same can be said for that of a writer who understands the context of their story well enough to doodle their vision on paper. I design quickly and efficiently when I start from code. And it shows in the end result. It is often stark, linear and lacking of anything truly distinct upon initial inspection. I design with more empathy and articulate information differently when I work with visual information first in an attempt to tell a story or create an experience. This may include starting with pencil and paper before using a computer. I'm surprised daily, by those who are lucky enough to be successful at both.
Graphic designers generally have a concise message they want to communicate and might employee an illustrator to help create elements that solve the design problem. Keep in mind, unlike the design field, Illustration only implies a method or type of visual element–a representative style or technique. This varies from talent to talent. Design utilizes a set of standards generally established and considered to be a rule(s) for communicating clearly and effectively to a large set of narrowed perspectives. A designer may decided that an illustrator's style or technique will enhance or even solve the design/communication problem.