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 TIFF?

The format print shops, scanners and archives run on. Lossless, capable of holding several images in one file, and old enough that everything in that world reads it. Files are large, which nobody in print has ever minded.