There is a third diamond shape that works in much the same way as the other two. In this diagram, Blue at 1 tried to prevent Red from connecting A to the lower left fence. Red plays 2, and as shown is guaranteed to connect.
The connection is called the Thin Diamond, because of its narrow shape. Where the long diamond encloses three intersections, and the square diamond encloses four, the thin diamond encloses only two intersections. The thin diamond allows you to jump the diagonal of a 3×3 square in any direction.
It’s interesting to note that in this situation, all three diamonds are available to Red. The thin diamond, as shown, is formed by playing at 2. The long diamond is formed by playing at B instead of 2. The square diamond is formed by playing at C, but note that in this case the square diamond does not guarantee a connection, because blue could block both paths with one move.