I'm unsure, depends on whether you're talking about the Japanese SMB2 or the American SMB2, which are both completely different games. The Japanese SMB2, also known as "The Lost Levels" is just the same game as the first, but with slightly different tilesets, Poison Mushrooms, and Warp Zones that took you backwards. It was deemed "too hard" by NoA so it wasn't released in the US until years later in it's Super Mario All-Stars form (when it was really just the same game as the first but with slightly more features added).

The American version of SMB2 was a re-skinned version of the Japanese game "Doki Doki Panic" with more "Arabian Nights" looking player characters being replaced with Mario characters, and interestingly, was released in Japan later on as "Super Mario USA." Many of the enemies from this game such as Shy Guys and the character of Birdo would become staples in later Mario games.