No, they aren't quite "the same". They're just different ways of referring to the same thing. If you look on the main site, you can see that each FF has its own section. If you go into the sections, you can see that the FF's you're wondering about are different. To sum it up, if you don't feel like looking:

FF2 is the one where you don't have levels. The NES version was not released in North America, but it was re-released in North America as part of FF Origins, for PSX.

FF3 is for the NES, and is the first FF where you can change your job. It was never released in North America, so you'll have to get an emulator if you want to play it.

FF4 is the one with the Dark Knight, Cecil. It was released in North America both for the SNES (under the name FF2), and as part of FF Chronicles for PSX.

FF6 is the one with Espers and the green-haired girl, Terra. It was released in North America for the SNES (under the name FF3), and as part of FF Anthology for PSX.

Note that in the case of FF4 and FF6, they really are FF4 and FF6. They were just called FF2 and FF3 because they didn't want to confuse North American consumers. Look where that got us now, though. =P