Super Mario World (also known as Super Mario Bros 4) is the first game on the SNES.
The gameplay is much more open-ended than it's predecessors, as unlike Super Mario Bros 3, you aren't confined to one map per world (and the world system isn't in this game), rather, all maps are connected to each other, and the player can visit any map that they want. The game also introduces the switch block palaces, which the player can go, and change that block type to be solid.
NES Version Edit
There was a version on the NES, by Hummer Team. Who also made Somari. This version has less levels, less music, and different/glitchy physics.
Game Boy Advance Remake Edit
The Game Boy Advance remake was part of a GBA series called "Super Mario Advance", which had most of the classic Mario games (except for Super Mario Bros) remade on the GBA.