The Tagged Image File Format (TIFF) is a very flexible image format which was created by Aldus Corporation to save images created by scanners and image manipulating programs. It usually uses an 8 to 16-bit per color channel storage method without losing image data. A disadvantage is that it creates very large files. Typically an image from a 3-megapixel camera will take up more than 9Mb of space on your storage card.
There are some variations in compressing TIFF files so you may have problems opening one from another source. Some use the LWZ (Lempel-Ziv-Welch) algorithm that is compatible with most applications.
The GIF format (Graphic Interchange Format), can only show 256 colors but it can choose any of the 16 million colors in a 24-bit image. These colors are stored in an index. It uses the LWZ lossless compression scheme also found in some TIFF files, however all GIF formats use the same algorithm so images can be transferred between different applications without any compatibility problems.
Since GIF handles images with a lot of contrast and fine details well, it is frequently used for line art such as cartoons, logos and text, and not so much for photographic images because, unlike TIFF, its resolution is really only appropriate for screen viewing.