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 TGA?

Targa dates to 1984 and refuses to die, because game engines and 3D packages standardised on it for textures and never had a reason to move. It keeps an alpha channel, optionally compresses runs of identical pixels, and is simple enough that every tool reads it.