In astronomy "seeing" refers to how stable the air is. Poor seeing is caused by turbulent air bending the light from the object.
@ElectricMink haze is covered under transparency. Light pollution with sky brightness. Clouds and fog are usually described with four letter words...
I always understood "seeing" as a catch-all that encompasses everything that can degrade the view? Atmospheric stability, haze, cloud cover, light pollution, fog....?