On the left is game's number and system in Japan. On the right is what the game was released as in America. If the game has been a part of a compilation pack, that's been added as well.
Final Fantasy (Famicom) - Final Fantasy (NES/PSX/GBA)
Final Fantasy II (Famicom) - Final Fantasy II (Final Fantasy Origins [PSX], Final Fantasy I+II Advanced [GBA])
Final Fantasy III (Famicom) - Not released in NA
Final Fantasy IV (Super Famicon) - Final Fantasy II (SNES), re-released as Final Fantasy IV (Final Fantasy Chronicles [PSX])
Final Fantasy V - Final Fantasy V (Final Fantasy Anthology [PSX])
Final Fantasy VI - Final Fantasy III (SNES), re-released as Final Fantasy VI (Final Fantasy Anthology [PSX])
Final Fantasy VII - Final Fantasy VII (PSX)
Final Fantasy VIII - Final Fantasy VIII (PSX)
Final Fantasy IX - Final Fantasy IX (PSX)
Final Fantasy X - Final Fantasy X (PS2)
Final Fantasy X-2 - Final Fantasy X-2 (PS2)
Final Fantasy XI - Final Fantasy XI (PS2/PC)
***
Basically:
Final Fantasy II on the SNES is really Final Fantasy IV.
Final Fantasy III on the SNES is really Final Fantasy VI.
They neglected to localize the other games and didn't want to mess up the numbers. They said, "Screw it!", however, when they got to VII. Then, of course, they switched to the games actual number.
As Square has been re-releasing the games on the PSX, they've also changed the numbers back. So IV is again IV instead of II and VI is VI rather than III.
Games released in NA and the systems they have been on:
FF (NES/PSX/GBA)
FFII (PSX/GBA)
FFIV (SNES/PSX)
FFV (PSX)
FFVI (SNES/PSX)
FFVII (PSX)
FFVIII (PSX)
FFIX (PSX)
FFX (PS2)
FFX-2 (PS2)
FFXI (PS2/PC)
Hope that cleared it up for you
*shrugs and walks away*