There are two types of pumps: centrifugal and submersible.
Centrifugal pumps are installed outside of the rainwater catchment cistern, typically inside of some sort of pump enclosure. While a pump motor can be loud, typical centrifugal pumps have a low noise level. In addition, if the pump is installed inside a pump enclosure, the enclosure can help to deaden the noise from the pump
Submersible pumps are installed inside of the rainwater collection cistern. Obviously for this type of pump, the noise volume is very low since the rainwater and the cistern will deaden the noise from the pump.
For a more in-depth, detailed answer, go to our FAQ blog post.