Why the difference, you ask.
Well, vörtbröd usually is baked into loafs, like the second example. Torbjörn Åhman, however, makes his using a “recipe from Bohuslän”. Perhaps the people of Bohuslän just prefer their bread made this way?
Hönökaka, a variety of bread commercially available in Sweden, originates from Hönö in Bohuslän, and is similarly shaped.
However, I would think tradition is the real reason for the thin shape. In the old days baking wasn't done very often, so the bread had to last long, and drying the bread was a solution. Therefore the cakes were made thin, so they would dry out quickly. They were also made circular, with a hole in the center, allowing the bread to be hung on long poles under the ceiling.