It is quite common to have multiple layers of water and each layer has a different clarity. Horizontal and vertical visibility is often very different from each other. When I estimate visibility, I am trying to describe horizontal visibility. When it is clear and I am talking about vertical vis, it is nice to report top to bottom, meaning I can see clear distinction between dark and light materials from the surface.
Physical oceanography is most concerned with vertical visibility since this is related to light penetration and the consequent potential for photosynthesis; I think anyway. I estimate horizontal visibility as distance I can clearly see a diver, but I can often detect a stream of bubbles from a greater distance than I can make out the diver. At night, a light shined from a distance toward my eyes can be seen considerably farther than what I would describe the visibility to be.