Don't they pour down just the same amount of water at the end of the day?
I mean in the tropical countries.
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And of course, anything in between.
The amount of precipitation that you get varies; it is not true that you always get the same amount of water and it is meaningless cherry-picking to compare different rains just because they produce the same total amount of water. Rains are usually started in regions where enough moisture and upward motion is present. However, depending on the situation, the humidity may differ, and so may the pressure gradient and temperature gradient.
At a certain pressure and/or temperature, droplets start to form, grow, and fall. The greater the pressure gradient (pressure difference between two points separated by a fixed distance) is, the bigger chance that you get speedy, heavy rains. So heavy rains often come with hurricanes - when the pressure gradient is large, and so is usually the wind speed. Fast rains also become more likely when the temperature gradient is high - the temperature strongly depends on the location. However, there are also many other factors that influence the character and strength of rains. For example, very heavy and fast "torrential rains" have been linked to the solar activity although the link remains somewhat inconclusive.
You may want to read the Wikipedia article about rain:
It also tells you how the rain is usually classified and what are the typical geometries at different places that lead to rain - things depend on the altitude, mountains around, latitude, and other things. The atmosphere is a complex system and the character of rains is determined by pretty much all of its complexities.