Direct injection or Turbo Direct injection (TDi) is a different kind of diesel fuel injection system that is more efficient than indirect injection.  Direct injected motors produce more noise and heat than indirect engines which is why direct injected engines weren't found until the late 70s and have not become widely available until the 80s.  However, direct injected engines and turbo direct injected engines are now widespread and have been built to control noise is some applications and are generally more efficient.

Indirect Injected engines utilize a fuel "pre chamber" where the fuel is "swirled" before it reaches each cylinder, allowing the diesel to combust completely.   

See this page on injectors for more information.