The REAL Super Mario Bros. 2 that we never got for two reasons:
1. It was too similar to the original.
2. It was Kaizo Mario before Kaizo Mario was cool.
For these two reasons, the folks down west said no, and stole one of Japan's games and made it into the SMB 2 that we all remember.
Despite its infamous reputation, The Lost Levels is actually not a bad game -- but it is very frustrating. The last two levels of the original game will probably take you several hours, and world C-4 is damn near impossible without cheats.