Terminology for hurricanes based off of rainfall

AIUI, the “Categories 1 through 5” for hurricanes are based solely off of wind speed and nothing else. Is there a category title for classifying hurricanes based off of amount of rain?

Also, is it possible to have slow wind but lots of rain, or are hurricanes usually high-wind high-rain or low-wind low-rain but not one high and the other low?

Saturation or condensation is the first step in the formation of precipitation but not enough by itself to cause precipitation.

In general you have to have some type of lifting for precipitation and typically that is through air bodies being forced over mountains, warmer air being forced over colder air or through convection.

With low pressure like a hurricane, air rises into the atmosphere where it cools and condenses and results precipitation. The ground level wind speed is not required for heavy rain but a rapid vertical speed is. The extreme vertical rise in a thunderstorm is an example of a situation where you may have lower surface wind speeds but large amounts of rain.

In the case of a low pressure system like a hurricane ground level wind strengths would typically be associated with precipitation amounts.

Also, for storms like Florence this year, and Harvey last year, what led to devastating rainfall totals was the extremely slow movement of the storms once they made landfall (as they effectively sat over areas and just continued to dump rain), not just the strength of the storms alone.