it's one of those rules deep in the rulebook you have to dig deep to find.
If a kicked ball does not cross the line of scrimmage, it can be advanced by the kicking (offensive) team.
However, once a kick ball crosses the line of scrimmage, only the returning (defensive) team can advance the ball.
But!!!!! once a returning team member touches the ball, both teams can advance it.
Unless, the punt is muffed. Then if the kicking recovers the ball, the ball can not be advanced.
Also, if the kicking team touches the punted/kicked (as a FG) first down field it is actully an illegal touching. The returning team can then pick up the football and return it without penalty or chance of losing the ball. If the return team does fumble the ball after the illegal touching by the kicking team, and it is recovered by the kicking team. The return team is awarded the ball at the spot of the illegal touching.
Did you all get that??????