Yes. They are different file formats (and their file extensions).
Wikipedia entries for each of the formats will give you quite a bit of information:
- JPEG (or JPG, for the file extension; Joint Photographic Experts Group)
- PNG (Portable Network Graphics)
- BMP (Bitmap)
- GIF (Graphics Interchange Format)
- TIFF (or TIF, for the file extension; Tagged Image File Format)
Image formats can be separated into three broad categories:
- lossy compression,
- lossless compression,
- uncompressed,
Uncompressed formats take up the most amount of data, but they are exact representations of the image. Bitmap formats such as BMP generally are uncompressed, although there also are compressed BMP files as well.
Lossy compression formats are generally suited for photographs. It is not suited for illustrations, drawings and text, as compression artifacts from compressing the image will standout. Lossy compression, as its name implies, does not encode all the information of the file, so when it is recovered into an image, it will not be an exact representation of the original. However, it is able to compress images very effectively compared to lossless formats, as it discards certain information. A prime example of a lossy compression format is JPEG.
Lossless compression formats are suited for illustrations, drawings, text and other material that would not look good when compressed with lossy compression. As the name implies, lossless compression will encode all the information from the original, so when the image is decompressed, it will be an exact representation of the original. As there is no loss of information in lossless compression, it is not able to achieve as high a compression as lossy compression, in most cases. Examples of lossless image compression is PNG and GIF. (GIF only allows 8-bit images.)
TIFF and BMP are both "wrapper" formats, as the data inside can depend upon the compression technique that is used. It can contain both compressed and uncompressed images.
When to use a certain image compression format really depends on what is being compressed.
Related question: Ruthlessly compressing large images for the web
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