first game to give you a high bounce from jumping on enemiesZero improvements, no changes, just more of 1 with unnecessary difficulty changes.
first game to give Luigi distinct physics
first game to add the flagpole trick for extra lives
first game to implement the full ending BGM
first game that awards the player a final congratulatory bonus stage for 100% completion
first game to add a real second quest
proto-autoscroll levels show up for the first time here
is at least somewhat visually distinct from its predecessor in their original 8-bit incarnations
bigger levels, more complex levels, occasional branching paths, and no reused levels; probably twice as much content as the first game
Not all of the above are super important, but this game doesn't get the respect it deserves for the series staples that it did bring to the table.
And, most importantly, it utilizes the foundation of its predecessor better than its predecessor did.