This is not a torus

The second diagram is not a Torus because notice that your picture is also telling you to glue together the two instances of the edge $be$, which we would usually not do when creating a Torus. Similarly with the edge $cf$. In the first part this is avoided by carefully creating enough edges in the interior so that this problem does not occur.

Geometrically what this is doing is taking two parallel circles along the tube of the torus and flattening (pinching) each to a flat line. The picture below demonstrates this beautifully: