Tees - I think we have established that to all intents and purposes, fog is cloud on the ground (my aviation met book from the Met Office agrees). However since the cloudbase is a vertical measurement from a cloudbase recorder and indicates where the thickness of the cloud (highest relative humidity probably) is sufficient to reflect the light or laser and the horizontal visibility (RVR in this case) is measured using a transmissometer over a fixed range (usually 200m) they are not stricly comparable - one is a reflected light measurement and the other a measure of the transparency of the air using a one way light transmission.
If you could measure horizontal and vertical visibility in flight you would always get variations as cloud is not a homogenous mass and has variations in relative humidity giving variations in visibility.