Hideo Kojima has officially confirmed that The Phantom Pain and Ground Zeroes are the same game... and that game is Metal Gear Solid 5. 

Kojima's session at the Game Developers Conference started with him coming out with bandages on his head to resemble Joakim Mogren the fictional CEO of Moby Dick Studio.  Up until the press conference, Konami had maintained that Moby Dick Studio was developing The Phantom Pain.

That stopped, however, when Kojima rolled out a video showing the connection between the two titles, as many had already speculated on in the past.  The trailer ended by showing the title Metal Gear Solid V: The Phantom Pain.

The trailer itself (which can be viewed here) includes a lot of images that were in previous trailers for Ground Zeroes and The Phantom Pain.  However, the new images suggest the presence of Revolver Ocelot and the words "FOX vs. XOF" and finally "A Phantom Battle Waged by the Vanished"... we'll let you watch the trailer to speculate for yourself what it all means.