The penalty kick is a kind of penalty used if and only if a team commits an offense warranting a direct free kick inside its own penalty area, in which case, a penalty kick is used instead of the direct free kick. As this does not apply to indirect free kicks, nothing is special there.
The only special case here is that there are specific offenses warranting an indirect free kick which apply only inside your own penalty area; those are specific for the goalkeeper. (Not that those offenses would be handled specially inside the penalty area, just that they cannot occur anywhere else by definition/plain logic.)
Therefore, an indirect free kick inside the penalty area is awarded to the attacking team if either
- the goalkeeper of the defending team commits any of the following four offenses:
- controls the ball with his hands for more than six seconds before releasing it from his possession
- touches the ball again with his hands after he has released it from his possession and before it has touched another player
- touches the ball with his hands after it has been deliberately kicked to him by a team-mate
- touches the ball with his hands after he has received it directly from a throw-in taken by a team-mate
- or if any player of the defending team
- plays in a dangerous manner
- impedes the progress of an opponent
prevents the goalkeeper from releasing the ball from his hands (which is obviously impossible inside your own penalty area)
- commits any other offence, not previously mentioned in Law 12, for which play is stopped to caution or send off a player
I believe indirect free kicks for the “generic” offenses are quite rare in penalty area; the offense would usually be either ignored completely, or a “similar” offense warranting a direct free kick and therefore a penalty kick would be ruled instead, etc. However, these do happen. A quick example video found with Google: during the 36th minute of Real Madrid CF vs Sevilla on April 29, 2012, Fazio played with a high foot on Ronaldo inside the penalty area, and an indirect free kick against Sevilla for playing in a dangerous manner was awarded. See this YouTube video: Free kick inside the penalty box ? Real Madrid v Sevilla 29. (Please disregard the confused/mistaken title and some comments).
And note that there is one specialty regarding the procedure for an indirect free kick awarded to the attacking team: If the indirect free kick was awarded inside the goal area, the kick must be taken on the goal area line parallel to the goal line at the point nearest to where the infringement occurred.