[gattilorenz]

I think that another factor is that they have quite different effects in day-to-day life. If it's cloudy you can still do most of the stuff you would normally do, but you wouldn't want to ride your car/horse/chariot/whatever at full speed in a foggy day (and in general, things that require good visibility). It's a useful distinction.

I'm not familiar with the Portuguese climate, but is fog somewhat common? If not, that might be a reason why you never felt the need for a word expressing the concept.