Part of the issue here is the mix-up in terminology. For us, the receiver is the square hole in the rear of the jeep that accepts the hitch. The hitch is a piece of angled metal that has the ball that the trailer rides on.
What do you have?
Is the hook you are talking about on the left side of the rear just below the bumper? If so, this is a standard recovery hook that comes on all JKs, and should not be used for towing.