Photoshop is raster-based and uses pixels to create images. Photoshop is designed for editing and creating photos or raster-based art. When the program was developed it was for photographers, but over time the program has grown to help all kinds of artists to do many different kinds of work. Now Photoshop is known to create interface designs, web pages, banner ads, video graphics, and the original use of editing and creating images for print.
Photoshop is known to be able to do so much and be so easy to learn that it is looked at as a one stop shop, but Photoshop is not the best program for all types of artwork and design.
Illustrator works off vectors, these are points used to create perfectly smooth lines. This program is for creating and editing vector-based work such as graphics, logos, and other design elements. Vectors are scalable images that can be sized as small or as large are you need them to be, but look the same when it comes to clarity and resolution.