Topic on Talk:Final Fantasy XIII
Exclusive fullscreen does not count as borderless.
An easy test for borderless is to open some windowed program (e.g. Calculator) while the game is running. A game running in borderless windowed mode will remain visible behind the windowed program whereas a game running in exclusive fullscreen will be minimised when the focus switches to the other program.
Some games don't have a dedicated borderless option, instead hiding the normal window border when the desktop resolution is selected in-game. A few games use borderless by default, and some don't have an exclusive mode (e.g. all WinRT games from the Windows Store).