I'm actually in Illustration, getting my BAA in it. I think wikipedia has a good definition:
http://en.wikipedia.org/wiki/IllustrationSo no, drawing is not pencil and illustration computers. Illustration can be a drawing, a painting, an etching, whatever but it's more about the information the image can convey. You can't compare drawing vs illustration really, since drawing is a part of illustration. I have to take a lot of drawing courses in illustration, since for any art you need a strong foundation. Any good illustration course will stress drawing, painting, traditional media in the beginning over digital since it gives you a much stronger foundation. It's more illustration vs fine art that's comparable than drawing vs illustration.
So.... if you want to take illustration, take both. You need a strong drawing foundation to do illustrations.