A half contortion is a pattern done with one arm wrapped around the back, and reaching forward between the other arm and the torso. If the right hand is wrapped behind the back, it's still positioned to the right of the left hand, in between the left arm and the left side. All the throws and catches done by that hand are made in this position.
In the full contortion, both arms are wrapped around the back and the pattern is still juggled in front. This restricts the movement of the arms so that the throws have to be made accurately using the wrists.
A body wrap or armpit throw is a front-to-back contortion throw: Instead of reaching across behind your back and sticking your hand between your arm and torso to throw in front, you reach across in front of your body and stick your hand between your arm and torso to throw behind your back, and the object comes forward over the shoulder on the same side as the hand it was thrown from.