I have a BFA in graphic design (got out of the field since I am much better as a tech). From all the courses I took in college, I have a broader knowledge base then just artists. Design encompases many disciplines into itself, among them photography, illustration and painting. Most, if not all, designers that have gone through college in the past decade should know how to use the applications to complete their designs. If not, then they are a dying breed which take 3x as long to complete their projects.
I remember going through college, and having a class that doesn't even exist now. The professor was very old school and had us do mechanicals for everything. This was after we had already taken our computer course. It seemed stupid to me, so I went and used the computers to set type, as well as compose as much as possible, then shot stats of everything (waste of time). That was the last time I ever had to do that and was back in 89 (damn, has it been that long already??? sheeeeesh).
These days with the high resolution printers (on desks), large volume full color printers (counts in the hundreds of thousands) and being able to go direct to plate, mechanicals are a definate thing of the past. Still, I remember (sort of) how to do things old school.
I guess the bottom line is a graphic designer knows how to do many things, all of which help to make a design work. An artist, typically, has one, or two, disciplines that he/she works with (i.e. illustrating/painting or photography...). I have a friend from college (art director/lead designer at the college paper now) that is an excellent illustrator. He also produces about 80%+ of the pages in the paper every week. I forget what his degree is in, since he graduated a couple of years before I did, but he is one of the most talented people I know. It almost makes me sick the things he can create either by hand, or computer (does some wild sh*t with Poser). I will see about getting some urls that have samples, just to show, later.