What is BMP?
The Windows bitmap, which stores pixels raw with no compression worth mentioning. Files are enormous. It survives because it's trivial to read - if you're writing an image loader from scratch or feeding an embedded display, BMP is the format that needs no library.
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.