GIF, or Graphics Interchange Format, was created by Compuserve in 1987, because they needed a platform that

would convert images small enough so that they could transfer pictures quicker across the slow connections of that time.  This

program compresses the file size to the point to which it doesn't lose data, or distort the image.  The program uses LZW

compression, which does so at a ratio of between 3:1 and 5:1.  GIFs can shrink down to as much as the repititon of the image

allows it.  For example, flat color, can have as much as forty percent compression.

            Even though GIFs sound like a good thing, they have its setbacks. For example, they are limited to a palette of 256

colors or less. Compuserve wanted to produce a 24-bit version of the already 8-bit GIF, but another company, Unisys,

discovered that they owned part of the technology.  As a result, they demanded fees to anyone who was using the format. This

means that there hasn't been any improvements on the GIF since Unisys came found out about their patient infrigement in 1994.

            JPEGs compress in such a way in which it throws away parts of an image, which is defined as "lossy". This is why it

loses far less information than GIFs. Even so, the ending result is somewhat a distortion from the orignal. The JPEG, or Joint

Photographic Experts Group, compresses in a five step process, which basically divides the image into squares.  This

compression can be as much as a 25:1 ratio.

These links are where I found my information:

Source1
Source2
Source3

Here are some examples of different JPEG and GIF settings on a few images.  See how they differ:

Clip Art Examples
Photo Examples
 

Thanks for checking out my site! :)