A muffed punt differs from a fumble because the muffed punt cannot be advanced when the recovery of the football is made in The American National Football League.
In the case of a muffed punt, it is possible for the punting team to recover the ball and continue the drive, but at least in NCAA and NFL rules, they cannot advance the ball on that same play. In the case of a fumble, the ball is live and can be returned by the team that recovers the ball. 
