A graphic designer is involved in any visual project that use typography, photography, illustration and layout. That doesn't mean he takes his own photos or draw their own illustrations. 99% of the time they don't.
An illustrator is the person who creates any visual piece that cannot be made with photography. The definition is short but it resumes well how large the term could be. If you paint over a photography or just add a texture over a photo, it IS illustration, not photography anymore.
An artist is a global term...what is art? Art is what you decide. Many illustrators consider themselves as artist, it's a personnal choice. I dont know for Travis, we should ask him
What I do and what Travis does is digital illustration, we use photos, scans, mix medias. In half of my work, I told myself : That is art, not illustration, sometimes it's very personnal and introspective, and seeing it that way, it's most considered as art.
Prestige (in this thread) was right about how graphic designer dont use computers. In my college years I almost never touch a computer even if Photoshop existed at that time. Why? we can work without them : We learned to draw our own types, scan and print photos, I made some layout using traditionnal ways. Today is a bit different, I never use traditionnal ways anymore, way faster with a computer.
Finally, there's 3 categories of graphic designer :
-Technical designers (they make magazine layout, advertising), -designers (
http://www.artofwong.com/) and -multimedia designers (mostly website, DVD/CD-Rom, VideoGame...)
The only graphic design part of my work is when I layout my illustrations and use vector logos to prepare it for the press. it's like...5% of my work maybe less.