The difference between Illustrator and Photoshop is pretty much moon and sun. Illustrator is a vector based application similar to the technical application of "Draw" as oppose to Photoshop which is distilled as a "Paint" application (Errr... old terms, but that's what they were called way back).Where as Photoshop uses raster files (Pixel based work with a fixed resolution) and uses .psd files primarily, Illustrator deals with vector work (Editable coordinates with multiple values that form shapes and lines, often used for graphic and design work} and uses .ai files. Whereas Photoshop might be the main gun of the same field as Paint Shop Pro or GIMP, Illustrator reigns in the same category as Freehand or CorelDraw.
Vector art has no fixed resolution, and is very editable as far as line work and simple shapes go, you can essentially get lines so perfect that only a computer could have drew them, but there are some heavy limits to what you can do in vector art alone unless you are extremely skilled.
Photoshop and Illustrator are sister programs respectively, so they compliment each other nicely, and between the two, you can do great work, but the reason a lot of people don't use Illustrator is the steep learning curve for using the pen tool and the elements of vector art.
Learning the Pen tool is 50% of learning to use Illustrator, so if you can handle it, Illustrator will be your right hand app of choice (You have to develop a feel for it though, kinda' like riding a bike). As Illustrator stands now, it has problems with line variation, and is designed for graphic and design work over and might not be what you are looking for if you are trying to hitch more expressive line art, but it has many benefits as well. So depending on your style, it's utilization may benefit you quite broadly.
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