Continuing Nick's answer, in the UK, we have lots of "fog" and "mist". "Fog" is much thicker than mist and it is much harder to see through it. "Mist" is common on winter mornings especially on higher ground or in wet areas like moorland or on meadows and heaths (wild grassy areas).

"Haze" is anything in the air that partially obscures vision. It's usually a light fog, but you can also have a "heat haze" when the air is hot enough to make things appear wavy. The word focuses on the fact that you can't see very well. "Mist", on the other hand, focuses on the fact that there's some stuff in the air - usually water, in the case of regular fog, but it can be anything that's visible. If you use dry ice, it produces some carbon dioxide mist/fog. "Fog" is the most common when talking about the weather, but "mist" is more common in many other contexts.