Sunlight keeps its mix of colours
Clouds often look white in daylight because their droplets scatter the colours of sunlight roughly equally. The mixture reaching our eyes still looks white. The Met Office explains this difference between clouds and blue sky.
In clear air, tiny molecules scatter blue light particularly strongly. The water droplets in a cloud are much larger, so they do not pick out blue in the same way. A white cloud against blue sky shows two different kinds of scattering side by side.
Why the bottom can look grey
Picture a cloud with a bright top and a darker underside. Sunlight is scattered many times as it travels through. Much of it leaves through the top or sides, so less reaches and emerges from the base.
NOAA also explains that sunlight diminishes as clouds thicken, so a thicker cloud can have a darker-looking base. The light has a longer, more complicated journey through it. Grey does not mean that the cloud has filled with grey water or soot.
It also does not mean you can predict rain from one patch of grey alone. This explanation concerns the light reaching your eyes, rather than a complete weather forecast.
The light itself can change colour
White is a useful description for a sunlit daytime cloud, not a promise for every hour. Near sunrise or sunset, the light arriving at a cloud can already look orange or red after travelling through more atmosphere.
The cloud scatters that changed light too. That is why the same familiar cloud shapes can glow warmly in an evening sky. Connect this with why sunsets are red, then compare the blue of clear air.