No, they aren't. Sonic 3 and Sonic & Knuckles were developed as the same game. When the developers realized that they were going to go over the deadline, they cut out half of the then-incomplete levels and split them into Sonic & Knuckles.
The data entries for the levels and music for Sonic & Knuckles are still in the level select/sound test of Sonic 3. Also, the idea of them both being separate games raises the question - why, then, do all of the Sonic 3 levels already have Knuckles' pathways built into them? Knuckles was planned to be playable in Sonic 3 from the start; they removed him and built him into the lock on feature in Sonic & Knuckles.
In essence, you actually had to pay for two games because the developers were too slow to finish it in time. It wasn't 'innovative', it was a last minute solution to solve the problem of "we spent way too much money making this game, we need to make it back somehow".
It's especially shitty that the games didn't turn out so great anyways.