Ah the Final Fantasy numbering saga. Let me lay it down.
Final Fantasy was released in Japan and the US. It did OK up here, but not well enough that they wanted to release Final Fantasy II and III. (Both of those were NES titles). When Final Fantasy IV came out, they decided to give the US market another shot. But they didn't want to confuse people in the US (Haha!) so Final Fantasy IV was released as Final Fantasy II. Final Fantasy V never made it to the US, so when Final Fantasy VI made it to international release, again, to avoid confusion, it released as Final Fantasy III. So at that point, Final Fantasy, Final Fantasy IV, and Final Fantasy VI were the only games in the states, and were known as Final Fantasy I, II, and III. When Final Fantasy VII came out, Square decided it didn't care about confusing people anymore, and released it as Final Fantasy VII. Every game from there on kept its original numbering.
Some people cling to the number that the game was released with, and some stick to the Japanese numbering, because every game is floating around somewhere now and it makes things less confusing.
Since the Japanese Final Fantasy II and III were NES games, for the purpose of this list, Final Fantasy II is always going to mean Final Fantasy IV, and Final Fantasy III is always going to mean Final Fantasy VI.
Clear as mud?