The frets could be somewhere alongside the neck. Some diagrams are in favor of vertically oriented, rather than horizontally. But they function the same way, just turn it 90 degrees clockwise. So, the answer is fretboard diagrams can be oriented vertically or horizontally.
Well, there isn't a single primary purpose for artists, as it changes from person to person. However, I would guess that it is to portray what they are feeling in that moment in time to people.
Hope this helps!!
