The US release "Final Fantasy II", is actually Final Fantasy IV
Canonically this is the fourth Final Fantasy game.
Neither Final Fantasy II or Final Fantasy III were initially released outside Japan, so Final Fantasy IV in North America was released as Final Fantasy II.
The US Final Fantasy releases were correctly numbered starting with the PSX releases.
From the game box:
Follow the dark knight Cecil - Lord Captain of Baron's elite force, the Red Wings - as he embarks on a fateful journey riddled with trials, betrayals, friendship, loss and self-discovery. Plagued with uncertainty over his monarch's motives, can Cecil turn away from the path of darkness and destruction?
User summary:
Final Fantasy IV was Square's first Final Fantasy installment for the SNES. The game was early planned to be released for the NES, but was quickly changed for a SNES release when Nintendo announced it, thus hitting the SNES RPG scene before Enix' Dragon Quest V did.
As playing RPGs was still something new at that time, Square made an attempt to get new players into the RPG gaming by releasing a special version called Final Fantasy IV Easy Type. The most notable differences included marking all hidden passageways with white spots; replacing all the specialized status restoration items with a generic "Remedy" item that healed all status changes; and removing many character abilities from the battle system. Also, the secret "developer team" room that lies hidden in the full game was not accessible in Easy Type.
Individual credits:
Hironobu Sakaguchi: Director
Nobuo Uematsu: Music
Yoshitaka Amano: Character & monster design
Microbadges: