Knuckles' jump was modified so that it reached the same height as Sonic would reach in Sonic the Hedgehog 2, but his mid-air mobility was slowed to give the gimped feeling his jumps had in Sonic & Knuckles. A fix was created to keep Knuckles' jump height consistent with that of the jump height from Sonic & Knuckles but also make the demos function properly.
Sega, though adjusting Knuckles' physics to match those of Sonic & Knuckles in-game, ran into issues with those same physics in the Sonic the Hedgehog 2 pre-game demos. This game is identical to Sonic 2 (aside from a few changes to make it more playable with Knuckles) but with Knuckles now playable instead of Sonic or Tails. The title screen features Knuckles also but removes the two player mode and options selections from it. Sonic is replaced by Knuckles and Tails is not playable whatsoever.
Knuckles in Sonic 2 is the resulting game when Sonic the Hedgehog 2 is locked onto Sonic & Knuckles with its passthrough port.