Slight showers: These may vary from scattered drops to drops falling fast enough to form puddles. The rate of accumulation in a rain-gauge is less than about 2mm per hour.
Moderate or heavy showers: Puddles form rapidly. In the heavier precipitation, you will hear a roaring noise on roofs and see a misty spray when the drops strike a hard surface. Visibility may be significantly impaired. Your rain-gauge will fill at 2-0mm per hour in a moderate shower and 10- 50mm in a heavy one.
Violent showers: Exceptional in the British Isles, but common in the tropics. More than 50mm an hour.
Slight rain: Scattered large drops or numerous small drops; not more than 0.5 mm per hour.
Moderate rain: Falls fast enough to form puddles rapidly. Downpipes flow freely. 0.5-4mm per hour.
Heavy rain: A downpour that makes a roaring noise on roofs, and a misty spray as it splashes on the road. More than 4mm per hour.
And the torrential rain we've been having over the past couple of days? Well that seems to be the one description for which no precise definition exists.