What is DDS?

DirectDraw Surface, which is how game textures are stored for the graphics card. Block-compressed so the GPU can read it without unpacking, and usually carrying a whole chain of mipmaps. Open a game's files and this is most of what you'll find.

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.