Since the mechanism for forming cloud is the same as that for fog ie the air must be cooled below its dewpoint to allow the water vapour to condense on the microscopic nuclei in the atmosphere - then fog is cloud.
As for the visibility of 1000m, that sets the boundary between mist and fog.
Driving in fog can mean anything from a few yards visibility to several hundred metres and the same is true of flying in cloud, you just can't measure it because (hopefully) there is nothing else but cloud up there with you.
As to the original question - another driving analogy - you should only drive as fast as the visibility permits you to see a hazard and stop safely - in the air you should stop flying VFR when your ability to 'see and avoid' is degraded by weather. When are you clear of cloud? - when you are not in it!