Here's my take on the differences between the file types:
BMP is an uncompressed and therefore "lossless" file format. It basically retains all detail and color information but creates a huge sized file to do it. A screen shot in SH1 or Crusader is over 2 megabytes in size, far too big for efficient use on the internet.The remaining three, GIF, PNG 8, and JPEG are all "lossy" formats, that is they use some form of compression to drastically reduce the size of the file, but must discard much of the detail and/or color information to do it. Applied appropriately, and when used (usually over the internet) for viewing on your computer screen, which is fairly low resolution, the results are quite good, often indistinguishable from a lossless format. These three formats use different compression schemes, making some better for certain types of pictures or graphics than others. The three have the most universal support in web browsers.GIF compresses quite well in many instances. For certain graphics and pictures it can yield much smaller and better quality results than JPG. The number of colors to use can be specified up to a maximum of 256. GIF is generally best for graphics with solid color areas. It scans horizontally, so any bands of color that go across the graphic will compress very well. GIF does not do well with gradients, as they tend to create banding. Photos are usually better in JPG, but not always. Simpler photos occasionally do better with GIF, sometimes smaller, sharper, and with better colors. GIF is also able to make the background color transparent which can be very nice looking if the graphic is of an object. It also supports animation. JPG cannot do transparency or animation.PNG comes in about 15 forms, PNG 8 and PNG 24 being the most common, which refer to the number of color bits they use. PNG 8 uses a maximum of 256 colors, similar to GIF. Its uses, file sizes, and results are similar to GIF, but files are usually smaller, especially for larger graphics. Certain forms of PNG can support true color (16 million colors). PNG does not support animation, but it does support background transparency. In fact it can go GIF one better since it can support up to 256 levels of alpha transparency.JPG (or JPEG) generally is the best choice for photos and screen shots, since they tend to have a large range of tonal values and may have gradients. When saving a JPG you specify a quality value between 1 and 100, 1 being the worst quality but smallest file size, 100 being the best quality and largest file size. Many graphics programs limit your choice to only a few of these settings, or even just one.While JPG usually creates small files it suffers from what is called "artifacting". JPG compresses using areas. The lower the quality the larger, therefore coarser, each area is, and you will see noticeable color changes, or artifacts (what look like out of place, different color pixels) between one target area and adjacent ones, and within each area. This is most noticeable in solid color areas, smooth tonal transitions, and especially around the edges of smooth color areas where they transition to a very contrasting color. JPG does best on photos or screen shots with very busy images, where nearby pixels constantly change color. In such an image the artifacting is less apparent, often becoming virtually invisible. Low quality JPGs also usually look less sharp than corresponding GIF or PNG images
File size comparison:These figures are for a screen shot taken in SH1 and Crusader with ALT-Q, and will vary considerably from program to program:
BMP = 2.359MB (original screen shot)
GIF = 745K
PNG = 334K
JPG = 122K - 1.473MB, depending on quality setting