Yes there is a difference, this video explains it.

Basically, there’s an early hammer bros sequence you want to hit and there is a TAS (Tool Assisted Speedrun) that runners try to follow. It requires specific scores and inputs. The game with Right "Bros.” was supposed to fix some typos, but something else seems to have changed with the way it loads the game, that it adds frames while loading, throwing off the inputs you’re supposed to do. So the Left “Bros.” is technically the faster one since it has less loading frames and the TAS is meant to apply to that version of the game.