TIFF is a lossless file format, the other two are not. TIFF can store grayscale, RGB color, false color, floating point and binary images. The other two are meant for storing color images - JPEG for RGB, and GIF for false or palletized color, and thus save gray scale images with RGB information, where R=G=B, or, perhaps in JPEG with data in only one color, zeros in the other two.
Both GIF and JPEG formats can sometimes save an order of magnitude or more in file space without an apparent loss in image quality. The temptation sometimes is too strong to avoid, but I would use caution in using either format for storing data that is to be processed later.
GIF is good for graphics, line drawings, lettering, and the like. Noise will drastically increase the file space for a GIF.
JPEG is good for photographs and shaded colors. JPEG sometimes smooths out noise in a useful way.
JPEG files typically show"twinkle" around lettering and around sharp edges. GIF files show color banding instead of smoothly graduated colors. This is shown in the three versions of the log-3-band color scale, in more-lx-images / Kratio-example /log-3-band.* The TIFF file shows the figure accurately.
They can be downloaded from http://www.nist.gov/lispix/images/Kratio-example.