They are worlds apart.
PS is a bitmap editing program, used primarily for editing photos, but it's also a capable drawing program.
Illustrator is a vector drawing program, primarily designed for graphic artists. Vector drawings can be enlarged infinitely without losing detail, bitmaps can hardly be enlarged at all without losing clarity. http://en.wikipedia.org/wiki/Adobe_Illustrator http://en.wikipedia.org/wiki/Photoshop
Ya so like he said Illustrator is for vector art which means you can expand of shrink the image infantry without losing quality. Photoshop is for photos and art that rely on pixels to make an image (if you zoom in far enough to a digital image you will begin to see individual pixels).
For Web Design you will often see more vector art because its great for things like logo design (you can have a little logo, or blow it up to a poster size without the loss of quality). Also if you have ever seen a flash movie (not like youtube but a cartoon movie in flash) all the frames are vectors (and you could zoom in and never see pixels).