The answer to https://scifi.stackexchange.com/a/17787/4056 mentions two different Batmans: Bruce Wayne (Batman) and Dick Grayson (Batman of Gotham City). What is the division of duties between the two? Does the Batman of Gotham City appear in anything besides Batman Incorporated? I have read the New 52 Batman and Detective Comics and the only Batman seen is Bruce.
That question and answer are about an issue from before retcon of the New 52. Bruce Wayne had gone missing and was presumed dead. In his place Dick Grayson (Nightwing) took up the mantle of the Batman. When Bruce Wayne returned, he designed a new costume for himself and allowed Dick Grayson to continue to operate as Batman protecting Gotham City (ergo Batman of Gotham City).
Because that panel (in the referenced question) is from Batman Incorporated, Bruce Wayne decided to franchise out the idea of the Batman to other cities. He is the CEO of Batman Incorporated, and so has a global influence of all training and operations involving Batman related heroes throughout the world. Dick Grayson is the primary Batman operator for Gotham City.
Under the New 52 Batman Incorporated, Bruce Wayne is once again the primary Batman character, with Dick Grayson operating as Nightwing.
When Bruce Wayne was pronounced dead, Dick Grayson took up the role as Batman and put Nightwing on hiatus. I think the difference in names is so people didn't confuse Bruce's Batman with Dick's Batman.
it's explained briefly in this video by Moviebob at around the 2 min mark: http://www.escapistmagazine.com/videos/view/the-big-picture/6191-Sidekicks