This is the 1994 Game Boy version, not the original 1982 arcade machine or any of the ports. It starts as if it was a simple port of the original game, but quickly becomes so much more than that. After you finish the first four levels you are taken to a map screen where you chase Donkey Kong in an attempt to rescue Pauline across groups of four levels. In the first three levels of each group you need to find a key, then carry it to an exit door. Each forth level is a boss fight against Donkey Kong.
I think this might be the first Mario game where he becomes acrobatic, you can do backflips, hand stand jumps, swing on wires etc. This is a couple of years before Mario 64 that I remembered as having introduced a lot of that.
The game is excellent, one of the best Game Boy games and definitely holds up.