A Granny Knot is basically an incorrectly tied Reef knot. On the Reef Knot page is a blue and red graphic representing that knot. A Granny Knot is similar, except for one thing.
In a Reef Knot, the two blue ends cross underneath the red loop on the right side and the two red ends cross over the blue loop on the left side of the knot. In a Granny Knot, the top blue end would be over the red loop on the right side and the top red end would be under the blue loop on the left side of the knot.
Also, the red rope part at the top of the knot would cross over the blue part of the rope, rather than under it.
The Reef Knot is criticized as an unstable knot. The Granny Knot is much, much more unstable and should never be used for any purpose.