Change

Title screen
The Doki Doki Panic screen starts off with three balloons, and each balloon pops and shows the title logo.


Intro
Doki Doki Panic's intro sequence is this: Two kids are reading a book, when a big green hand pops out and yanks them into the book. Their pet monkey runs off to find help. A family finds the book, then decides to jump into it and save the kids.
In Super Mario Bros. 2, the intro is just a story about how Mario dreamt about some weird land. Not too exciting.

Character Select Screen

In Doki Doki Panic, you choose your character at the start of the game and play all the way through with him/her, saving after you defeat a boss. So basically there are four save files, one for each character. In SMB2, you can pick your character after every level.


Bonus Chance

DDP's Bonus Chance screen is incredibly bland. Even though SMB2 used its Title screen as the background, anything's an improvement over DDP's screen. The cool thing about DDP's bonus chance is that the vegetables change depending on what level you're in. This would've been neat in SMB2, but, oh well.


Mariofied
These are all the items and characters that were changed from DDP to SMB2. The enemies were not changed, except for boss of 5-3.


The average brother was changed to Mario.

The high-jumping Mama was changed to Luigi. This is the first time that Luigi is depicted taller than Mario in a game.

The long-jumping sister was changed to Princess Toadstool.

The strong Papa was changed to Toad.


The grass changed from black to red. In SMB2, when you pull out the red grass, the vegetable you get will still have black grass on top.

The magic lamp that makes a door appear was changed to a magic potion.

The Heart that appears in certain areas of Sub-Space was changed to a Mushroom.

In DDP, the 1-Up item was your current character's head.

The Shell was some sort of black shrunken head thing in DDP.


This Inca mask thing was changed to "Hawkmouth."

The "BOM" explosion was changed to the English "BOMB."

Phanto looks less menacing in DDP.

The Mushroom Blocks were originally odd looking masks.

This veggie from World 7 was changed for some reason.


The Lost Mouser
Doki Doki Panic originally had three Mousers, the third one appearing at the end of World 5-3. The white Mouser was replaced by Clawgrip, a rock-throwing crab.


Above is a map of the third Mouser's chamber, which was completely replaced by Clawgrip and his stockpile of rocks (below). The four clumps of grass to the left of Mouser were bombs.


Comatose sprites
In Doki Doki Panic, not very many items were animated. For example, there are no animation frames for Cherries, POW Blocks, vines, grass, Crystal Balls, Bomb fuses, water, and spikes; the animation for these items were added for SMB2.

The Albatoss enemy also has fewer animation frames than its SMB2 counterpart. Phanto does not move when you pick up a key, but he magically appears later to chase you around.

In a somewhat related note, if you get down to one dot on the power meter in DDP, you don't shrink to half your size. This and the "B-Button run" are Mario trademarks, and were duly added to SMB2.

(courtesy of http://www.themushroomkingdom.net)

-Fyree the Spirit God

Super Mario Bros 2 in the US was later released as Super Mario Bros USA in Japan.