What is GIF?
Thirty-five years old and still everywhere, because it does one thing nothing else quite does: animate inline, silently, in any context that displays an image. The cost is a 256-colour palette and no real motion compression, which makes GIF a poor way to store video and an excellent way to send a three-second loop.
What is PGM?
Greyscale, uncompressed, with a header you can read in a text editor. PGM is part of the netpbm family, and it exists because sometimes you want pixel values you can do arithmetic on without a decoder in the way. Image processing and computer vision code loves it.