As an ATCO, I understand it as -
VV/// when there is fog, (which really forms when the wind is below 5kts and you have close to 100% humidity) and you cannot see the sky to determine what the cloudbase is.
OVC000 is used if we get the same effect in higher wind conditions (which can be up to 40kts here at Bristol). Then it's not textbook fog, but rather low cloud.