Foul Tip Vs. Foul Ball Catch

Question
At what point does a caught foul ball back to the catcher become an out even if it is caught from a bounce to the head of the catcher or a high backwards pop up that a catcher grabs after it strikes her body before she gains control?  Confused.  I do understand the foul tip rule.  Foul ball from bat to catcher's head and caught is foul.

Answer
A foul tip is a ball that goes directly to the catchers glove from the bat and is caught. It is treated just like a strike and the ball stays live.  If it is dropped it is a dead ball.  A tip that goes directly from the bat and hits the catcher or any part of their equipment is dead immediately when it hits the catcher and is treated like a foul ball.

So if the ball goes directly from the bat, hits the catcher in the head and then is caught you basically have the result of a foul ball because the ball became dead when it hit the catcher's helmet.

There really is no such thing as a caught foul ball.  The definition of a foul ball requires it to leave the field of play, touch the ground, touch a person or touch some piece of equipment or fence when the ball is on or over foul territory.  

If the ball is caught in the air and does not meet the definition of a foul tip it is simply a fly out credited to whoever caught the ball no matter where they are standing when they catch the ball.