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Various image formats are -
JPG is used when small file size is more important than maximum image quality (web pages, email, memory cards, etc). But JPG is good enough in many cases, if we don't overdo the compression. Perhaps good enough for some uses even if we do overdo it (web pages, etc). But if you are concerned with maximum quality for archiving your important images, then you do need to know two things: 1) JPG should always choose higher Quality and a larger file, and 2) do NOT keep editing and saving your JPG images repeatedly, because more quality is lost every time you save it as JPG (in the form of added JPG artifacts... pixels become colors they ought not to be - lossy).
GIF was designed by CompuServe in the early days of computer 8-bit video, before JPG, for video display at dial up modem speeds. GIF always uses lossless LZW compression, but it is always an indexed color file (8-bits, 256 colors maximum), which is poor for 24-bit color photos. Don't use indexed color for color photos today, the color is too limited. PNG and TIF files can also optionally handle the same indexed color mode that GIF uses, but they are more versatile with other choices too. But GIF is still very good for web graphics (i.e., with a limited number of colors). For graphics of only a few colors, GIF can be much smaller than JPG, with more clear pure colors than JPG). Indexed Color is described at Color Palettes.
PNG can replace GIF today (web browsers show both), and PNG also offers many options of TIF too (indexed or RGB, 1 to 48-bits, etc). PNG was invented more recently than the others, designed to bypass possible LZW compression patent issues with GIF, and since it was more modern, it offers other options too (RGB color modes, 16 bits, etc). One additional feature of PNG is transparency for 24 bit RGB images. Normally PNG files are a little smaller than LZW compression in TIF or GIF (all of these use lossless compression, of different types), but PNG is perhaps slightly slower to read or write. That patent situation has gone away now, but PNG remains excellent. Less used than TIF or JPG, but PNG is another good choice for lossless quality work.