FF series are made using SE's engine called "Crystal Tools". Final Fantasy Versus XIII is part of the Fabula Nova crystallis (wiki it). Its a series of 4 XIII games each in different time periods by tied together by a Crystal. Versus is more of a kingdom hearts style game play which some call an ARPG (Action RPG) but we have yet to see proper in game footage of how this battle system will work.

Wiki reference.

Fabula Nova Crystallis Final Fantasy XIII (ファブラ ノヴァ クリスタリス ファイナルファンタジーXIII, Fabura Nova Kurisutarisu Fainaru Fantajī Sātīn^?) is the collective name of a series of games made under the Final Fantasy XIII label by Square Enix. Made in the same vein as the Compilation of Final Fantasy VII and the Ivalice Alliance, Fabula Nova Crystallis (which means "the New Tale of the Crystal" in Latin) is based on various worlds and different characters, but each game will be "ultimately based on and expand upon a common mythos." According to Square Enix, they all take place in the same universe, but are not directly related to each other

There was 4 games planned for this series but its now only 3.

Final Fantasy XIII - PS360

Final Fantasy Versus XIII - PS3

Final Fantasy Agito XIII - PSP

Final Fantasy Haeresis XIII - Cancelled

Well explained man.