No. Not all offences in the penalty box lead to a red card.
Many offences within the penalty box lead to no further action than a penalty being given. The referee can also show a yellow card for offences within the penalty box. If the yellow card shown is the second one received by the player during the match, the player must be sent off.
Red (sent off) or yellow (cautioned) cards are to be shown for the following offences according to
FIFA Laws of the Game, Law 12: Fouls and Misconduct
A player, substitute or substituted player is sent off if he commits any of the following seven offences:
• serious foul play
• violent conduct
• spitting at an opponent or any other person
• denying the opposing team a goal or an obvious goalscoring opportunity
by deliberately handling the ball (this does not apply to a goalkeeper within
his own penalty area)
• denying an obvious goalscoring opportunity to an opponent moving
towards the player’s goal by an offence punishable by a free kick or a
• using offensive, insulting or abusive language and/or gestures
• receiving a second caution in the same match
Now it's up to the referee's discretion as to whether the offence falls within any of the above categories.
A player is cautioned and shown the yellow card if he commits any of the
following seven offences:
• unsporting behaviour
• dissent by word or action
• persistent infringement of the Laws of the Game
• delaying the restart of play
• failure to respect the required distance when play is restarted with a corner kick, free kick or throw-in
• entering or re-entering the field of play without the referee’s permission
• deliberately leaving the field of play without the referee’s permission
Again it is completely up to the referee's discretion to judge whether the offence falls under any of the above categories.