"There is fog on the street" should work fine. There is no reason why there could not be fog on one street and not elsewhere. Localized fog is very common especially in early morning or late evening in cool or cold seasons. It only requires a warm water surface with colder air above it and little or no wind. I have seen fog patches on streets, roads, and highways.
In my experience, "на улице" most often refers to a specific street unless the expression is necessarily general. An example of a general expression would be "на улице холодно" или "жарко на улице!"
I see where you're going with this. In English (disclaimer - in my particular area of English use :) since it varies!) - In English, we don't say, "It is fog outside." Fog is a noun. Instead, we describe this amorphous "it" with an adjective - foggy. So far we are on the same page, I think.
Now, whether this is stated in adjectives (туманно) or nouns (туман) in Russian is another thing altogether, something I can't answer and as ever we turn to native speakers such as yourself for help. What I think you're saying is that in Russian, you would prefer to say, "На улице туманно" to describe the weather as foggy, rather than say На улице туман which would mean that the weather is fog. Could both phrases be used in describing the weather?
The both phrases are used for describing the weather. If you want to describe the situation outside you can use the both phrases. If you want to say that it is foggy at some areas/cities (local fog) it is better to use the phrase with the noun.
In English, "it is fog" answers the question "what is it?" I suspect the Russian equivalent would "Это туман" answering the question "Что это на улице?"
In contrast, "it is foggy" answers the question "how is it?" or "what is it like?" Perhaps in Russian we could have a question and answer like "А как сейчас на улице?" - "Прохладно. На улице туман."
What a hot and fascinating discussion, folks ! I can't but add this version : "(The ) fog is outside ...."? https://www.tripadvisor.in/LocationPhotoDirectLink-g1162199-d2423527-i156314059-Nivant_Hill_Resort-Satara_Satara_District_Maharashtra.htmlhttps://blog.allstate.com/deal-foggy-windows/
Please, do not blame me too bitterly.