I don’t know why they have to be so confusing with game numbering sometimes. Teenage Mutant Ninja Turtles II: The Arcade Game was in fact based on the original arcade game. However, when the original arcade game was released in 1989, a different Teenage Mutant Ninja Turtles game was released at the same time for the NES. Hence when they released the one actually based on the arcade game a year later, they put a II in the title. The home computer ports just stuck with Teenage Mutant Ninja Turtles: The Arcade Game and left off the II.
The NES version is probably the best known port and included a couple of extra levels with new enemies and also extended many of the original arcade levels. The NES version also added some Pizza Hut product placement advertising. I believe that the computer ports (Amiga, Atari ST, Commodore 64, DOS, etc.) were more straight ports of the arcade.
The NES and arcade versions were especially good with most of the other versions being worthwhile as well. If you like arcade style games then this is one of the better ones from that era. And who can resist the Teenage Mutant Ninja Turtles?
