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The Difference Between
Photoshop
and Illustrator

There are two kinds of computer graphics - raster (composed of pixels) and vector (composed of paths). Raster images are more commonly called bitmap images.

In general, bitmap-based files require more computer memory for file storage than vector-based files.
Photoshop
Illustrator

Anti-Aliased Bitmap Image:
When shrunk, you can's see the artifacting...

Smooth Vector Image:

Bitmaps are best used for photographs and images with subtle shading.

Graphics best suited for the vector format are page layout, type, line art or illustrations.

A bitmap image uses a grid of individual pixels where each pixel can be a different color or shade. Bitmaps are composed of pixels.

Bitmap images require higher resolutions and anti-aliasing for a smooth appearance

Aliasing - aliasing occurs when a computer monitor, printer, or graphics file does not have a high enough resolution to represent a graphic image or text. An aliased image is often said to have the "jaggies."

Vector graphics use mathematical relationships between points and the paths connecting them to describe an image. Vector graphics are composed of paths.

Vector-based graphics on the other hand are mathematically described and appear smooth at any size or resolution.

From http://www.sketchpad.net/basics1.htm, http://www.mustek.com/class/bit_vec.html