Different enough where it counts.
For example, you can't just jump on an enemy to defeat them now. If you try that, you'll just ride on their back. To actually defeat them, you have to jump on them then pick them up and toss them, at other enemies if possible. Also you'll be plucking some of the numerous vegetables strewn around the level to defeat these guys. Sometimes you'll even get to use a POW Block, which causes a massive tremor defeating all generic enemies on the screen. You'll even pick up weird-looking potions that actually make doors (putting them in the right spot and stepping through will allow you access to some bonuses). And that isn't all.
At the start of each level, you can pick one out of four characters. Mario, Luigi, Peach, and Toad. You read that right. Peach isn't the kidnapper-target she was in the last game, in fact this time she's playable. If that weren't enough, many people will argue that she's the best character to use since she can float temporarily. Luigi will jump higher. Mario is average in all areas. Toad can dig faster than everyone else. Even though you'll probably use Peach the most out of all the characters, the others have their uses.
In fact, just about every area here is different from the original SMB, something most sequels don't do. Whether you, the player, can accept this fact or not will factor into how much you enjoy this game. Nothing more to say.