Sonic & Knuckles is an extension to the game Sonic 3. Apparently, Sega decided to split the game into two parts due to storage limitations. However, there's a few differences which makes it feel like it was developed separately.
In this game, you can choose to play as either Sonic or Knuckles (Tails has been removed). Sonic has the same abilities as in Sonic 3 I.e. he still has his spin-dash and the elemental shields. The Lightning shield enables Sonic to perform a double jump, the Water shield lets Sonic breathe underwater and perform a bounce-attack, whereas the Fire shield allows him to do a horizontal mid-air dash. Knuckles has the ability to glide and climb walls which leads to a more exploratory play style. Knuckles has a smaller jump but can reach places Sonic cannot due to his other abilities.
The levels are fairly large, but there's less of them compared to previous games. There are seven Zones in the main game; five contain two Acts each, two contain just one Act. When you reach the end of an act, you continue playing as if the world is all interconnected which is a really cool effect.
There's plenty of boss battles throughout the game, but boss battles aren't usually all that fun in platforming games. There's a larger variety in bosses compared to Sonic 3, so these bosses require different strategies to take down and are actually more fun to battle against.
There's frequent check-points scattered throughout the level which allow you to respawn at that position when you die. For some reason, the save feature has been removed, so you need to complete the game in one sitting. Modern versions of the game (such as Sonic Mega Collection) allow you to save mid-game anyway.
If you have 50 rings and pass a check-point, you can enter a bonus stage. There's also hidden large rings which take you to the special stage; although these are much harder to find compared to Sonic 3. This stage is rendered in 3D where you have to pass through blue orbs while avoiding the red ones.
The original cartridge allowed you to insert other Sonic games into it. The main idea was that Sonic 3 could be inserted to create the full game, allowing the use of Sonic, Tails or Knuckles to play through all the Zones. Inserting Sonic 2 allowed you to play through that game as Knuckles, whereas inserting Sonic 1 allows you to play more 'Blue Sphere' bonus stages.
Even though the game is a continuation of Sonic 3, it is surprising that the level design seems different. Despite people saying Sonic games were fast, one of my complaints with Sonic 3 was the slow speed. There's much more hazards in this game, so you proceed in a slower pace; therefore, this game is even slower than that. On the plus side, it seems more skilful, rather than just running and randomly jumping while hoping for the best. Some levels have different mechanics not seen in previous Sonic games such as switches you need to hit to open doors. The variety makes it a better game than Sonic 3, although the final three worlds are very dull, including the boss battles which feel repetitive.