It should be no secret by now, so let's get it out of the way first - Yes, the Super Mario Bros. 2 that most of us know, that is, this one, is technically not really a Mario game. Originally released in Japan as Yume Kōjō: Doki Doki Panic (Dream Factory: Heart-Pounding Panic), it was designed by Shigeru Miyamoto, and starred an Arabian-esque family of four instead of the cast you're familiar with.
The Super Mario Bros. 2 that Japan got was pretty much just a much harder version of the original Super Mario Bros., and, supposedly fearing that it would be too hard for the west, Nintendo instead decided to replace the protagonists in Doki Doki Panic with Mario characters (As well as some other small changes), and release it in the west as our Super Mario Bros. 2. Later, they then went and released the edited version in Japan as Super Mario Bros. USA!
As this game does not have its origins as a Mario title, you'll immediately notice some major differences from the rest of the series, starting before you even begin playing properly. You'll be presented with a choice between Mario, Luigi, Peach and Toad before every stage - All of them have their own strengths and weaknesses, so if you fail with one, you might be able to succeed with another.
When you actually gain control, you'll notice some more oddities. Jumping on enemies here won't immediately defeat them - instead, you'll simply stand on top of them and can basically ride them around. You can then press B to lift them up, after which you'll be able to throw them anywhere you want! Every level is also littered with tiny weeds that you can pull up in a similar manner to reveal throwable vegetables, bombs, potions that create magic doors which can lead to a variety of secrets, and more.
Levels in this game are generally quite a bit more complex than those in its predecessor and sequel. You'll have to find keys to unlock locked doors, blow up rocks with uprooted bombs, dig through sand pits to find items or pathways below, and even occasionally ride flying enemies or magic carpets to cross large chasms. You can also usually find several rooms that do not need to be accessed, but they can be nice to visit for extra health and other items.
Curiously, at the end of almost every single level, you'll have to deal with a boss, which is usually one of three different types of Birdo. After the fight concludes, or occasionally when there is no fight, you'll have to pick up the glowing ball that appears to open a large mounted hawk head, which ends the level and lets you play a roulette game for extra lives, provided you found coins. After the last level of each world (Of which there are seven total), you'll also have to square off against a slightly tougher boss, culminating in a fight against the final boss Wart, who surprisingly has not appeared in a single Mario game since.
Graphically and musically the game still holds up quite well. The game world is quite a bit more vibrant and feels more alive than that of the first Super Mario Bros., and while history proves that SMB2's main theme was not as memorable as the Mario theme, the game has a catchy soundtrack nonetheless, despite only having a few songs, much like the first title.
It's a bit of an oddball to players familiar with other Mario games, sure, but the fact that it's so different from the rest of the series is what makes Super Mario Bros. 2 such an entertaining game. If you want a fun but unusual Mario experience, look no further - this is pretty much the textbook definition of it.