Also, this is the grammar pattern (blunt form + it-da (sorry, no Keyboard on this computer))which indicates the current condition of something. So, as opposed to "It is getting foggy" this is more like "It is currently foggy". Another example would be the difference between "The door is opening / The door opens" and "The door is currently open".
By definition, fog and mist both describe a suspension of water droplets in the air. The difference lies in the density hence visibility. Fog is denser than mist.
Koreans use 안개 for both. In fact, 안개 is used for fog, mist, haze, brume.
Drizzle, 가랑비 or hazy rain, 는개 seem to be words decribing the dewy rain or fine precipitation of water which you mentioned.
That said, it boils down to common usage. 'Mist' is frequently used in spoken English language to mean 'fine rain' also; that which causes confusion.
To me, "it is misty" means that kind of fog that's drizzling down like lazy rain. Stuff outside will have a dewy layer and may develop droplets after a while. "It is foggy" just means you can't see past a certain distance because of "clouds" down at our level. Things aren't necessarily getting moist like if it were misty. Anyway, I'm wondering which of these the Korean phrase can refer to.