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 PNG?
PNG is the web's lossless image format. It compresses without ever degrading the picture and has a real alpha channel, which is why screenshots, logos, line art and anything with sharp edges or text belong in it. The trade is size: on a photograph, PNG is enormous compared to JPG.