Is Kingdom Hearts 2 the same as Kingdom Hearts final mix?

Officially, KH2's International Edition is called "Kingdom Hearts II Final Mix+" because they called the International Edition of the prequel "Kingdom Hearts Final Mix." So they added the "+" to avoid confusion.

KH2 Final Mix is the Japanese "International" release of the game. As in the version with Japanese text but English voiceovers.

Also Final Mix comes with a couple of new items/weapons, bosses, music, fmvs and levels. There is an additional disc which contains the PS2 remake of the Kingdom Hearts: Chain of Memories (the GBA game) which has also been similarly tweaked.