In any case, cloud, whether as fog or low cloud base had the same effect on flights.
Not quite. Low cloud, as long as it is above the coughpit height, may preclude you from landing off an approach, but, in general, as soon as you break out of the cloud, the visibility is acceptable for the landing. But, in the case of low vis ops, the cloud can actually go all the way to the ground.
Visibility, on the other hand, is always required to some degree (though as little as 75 metres for my low vis ops) and can be reduced by a number of factors. Fog, heavy rain, smoke.
Taxiing in the other morning, there was appreciable ground fog, and vis was certainly reduced, although at the time we landed I'd expect it was still quite patchy. It went lower by the time I got out of the terminal.
Melbourne does have a Cat II/III approach, but it is currently out of service. Rumour has it that someone cut the power to the high intensity approach lighting (which is mandatory for low vis ops).
The availability of the low vis approaches only avoids diversions if the conditions are forecast. Contrary to popular opinion, aircraft do not arrive in Melbourne with diversion fuel to Sydney or Adelaide as a matter of course, but will only do so if required. Having a Cat III will allow you to land off the approach, but you can't actually start it unless you have the diversion fuel. So, if the fog is unforecast, you will still need to divert, Cat III or not.
Low vis, autocoupled, approaches are only of use in foggy conditions. They are useless if it's a windy day.
