Generally these are either:
Lossless compression
Lossless compression algorithms reduce file size without losing image quality, though they are not compressed into as small a file as a lossy compression file. When image quality is valued above file size, lossless algorithms are typically chosen.
Lossy compression
Lossy compression algorithms take advantage of the inherent limitations of the human eye and discard invisible information. Most lossy compression algorithms allow for variable quality levels (compression) and as these levels are increased, file size is reduced. At the highest compression levels, image deterioration becomes noticeable as "compression artifacting". The images below demonstrate the noticeable artifacting of lossy compression algorithms; select the thumbnail image to view the full size version.
Each format is different as described below:
JPEG
JPEG (Joint Photographic Experts Group) files are (in most cases) a lossy format; the DOS filename extension is JPG (other OS might use JPEG). Nearly every digital camera can save images in the JPEG format, which supports 8 bits per color (red, green, blue) for a 24-bit total, producing relatively small files. When not too great, the compression does not noticeably detract from the image's quality, but JPEG files suffer generational degradation when repeatedly edited and saved. Photographic images may be better stored in a lossless non-JPEG format if they will be re-edited, or if small "artifacts" (blemishes caused by the JPEG's compression algorithm) are unacceptable. The JPEG format also is used as the image compression algorithm in many Adobe PDF files.
TIFF
The TIFF (Tagged Image File Format) is a flexible format that normally saves 8 bits or 16 bits per color (red, green, blue) for 24-bit and 48-bit totals, respectively, using either the TIFF or the TIF filenames. The TIFF's flexibility is both blessing and curse, because no single reader reads every type of TIFF file. TIFFs are lossy and lossless; some offer relatively good lossless compression for bi-level (black&white) images. Some digital cameras can save in TIFF format, using the LZW compression algorithm for lossless storage. The TIFF image format is not widely supported by web browsers. TIFF remains widely accepted as a photograph file standard in the printing business. The TIFF can handle device-specific colour spaces, such as the CMYK defined by a particular set of printing press inks.
PNG
The PNG (Portable Network Graphics) file format was created as the free, open-source successor to the GIF. The PNG file format supports truecolor (16 million colours) while the GIF supports only 256 colours. The PNG file excels when the image has large, uniformly coloured areas. The lossless PNG format is best suited for editing pictures, and the lossy formats, like JPG, are best for the final distribution of photographic images, because JPG files are smaller than PNG files. Many older browsers currently do not support the PNG file format, however, with Internet Explorer 7, all contemporary web browsers fully support the PNG format. The Adam7-interlacing allows an early preview, even when only a small percentage of the image data has been transmitted.
GIF
GIF (Graphics Interchange Format) is limited to an 8-bit palette, or 256 colors. This makes the GIF format suitable for storing graphics with relatively few colors such as simple diagrams, shapes, logos and cartoon style images. The GIF format supports animation and is still widely used to provide image animation effects. It also uses a lossless compression that is more effective when large areas have a single color, and ineffective for detailed images or dithered images.
BMP
The BMP file format (Windows bitmap) handles graphics files within the Microsoft Windows OS. Typically, BMP files are uncompressed, hence they are large; the advantage is their simplicity, wide acceptance, and use in Windows programs.
Use for Web Pages / Web Applications
The following is a brief summary for these image formats when using them with a web page / application.
PNG is great for IE6 and up (will require a small CSS patch to get transparency working well). Great for illustrations and photos.
JPG is great for photos online
GIF is good for illustrations when you do not wish to move to PNG
BMP shouldn't be used online within web pages - wastes bandwidth
Source: Image File Formats