Raster Graphics
Raster graphic images are made up of a grid of colored pixels and each pixel can be edited individually (although that would be a tiresome thing to do.) This is the best choice when photo editing and Photoshop relies primarily on this process. Raster graphics are commonly called bitmap images. In class, I always compare raster graphics to the old toy Lite Brite. Try playing with Lite Brite but don't forget to come back.
Vector Graphics
Now, Illustrator is mostly a vector graphics program. Vector graphics use mathematical relationships between points and the paths that are connecting them to describe your image. Vector images are generally found in drawing programs. I compare these graphics to a learning tool sometimes used in math classes called a Geoboards. (Try playing with a geoboard.)
Advantages/Disadvantages
There are advantages and disadvantages to each type of graphics and the choice you make should depend on what you are up to. Raster graphics are best with photographs and other images that require subtle shading. But to look good, bitmaps need higher resoltuion and anti-aliasing to in order to look smooth. When you resize a bitmap image you are likely to get some distortion and if you enlarge it too much, it will start looking pixelated and come down with a bad case of the jaggies. (see image below.)
If you are creating type, drawing line art, or simply needing some nice crisp edges to an image, vector graphics is the way to go. You can draw an itty-bitty teeny tiny image in a vector program and then scale it to 1000% and it will still as clear and crisp as the original. You don't get the same distortion with vectors as you do with bitmaps. I created the flower in Illustrator. The original was less than 1/2 inch. I then copied it and rasterized the copy. Next, I scaled them way up. Notice the jaggies on the raster image.
Raster Graphics in Illustrator
Although Illustrator is predominantly a vector program although there is nothing preventing you from rasterizing objects or placing a photograph in your design. Also, there are several Photoshop filters available in Illustrator. These filters are in the bottom half of the Filter menu. They will be grayed out unless you rasterize your object first. (Object>Rasterize) As a further challenge, you must also remember that the file's color mode must be RGB to rasterize the object. You can change color mode by choosing: File>Document Color Mode.
About Filter Menus
For a long time I didn't know about this rule and attributed the randomness of my ability to use filters to current atmospheric pressure. Notice that there are some filters in both the top half and the bottom half of the menu (style/distort). Normally, unless you are working with raster graphics, you will be using the filters on the top half of the menu.
So, those of you who have dabbled in both Illustrator and Photoshop, which do you prefer to work with--raster or vector graphics?

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