Clayfighter: Tournament Edition was a Super Nintendo exclusive fix of the original with many things changed, such as:
Most stages from the original were modified. The stages were either slightly edited, some redone from scratch.
Many glitches from the original were fixed. Notably, the glitch to play as N. Boss was removed.
Many new modes were added, more versus modes were added, since it is a 'tournament' edition.
The intro and title screen were edited.
Source: Wikipedia, "ClayFighter", available under the CC-BY-SA License.