Technically, a moon was a celestial body that orbits another celestial body. In common usage, "moon" referred only to those objects of significant size orbiting around a planet, although moons could also have moons. They were also collectively called "natural satellites", a term that could also encompass asteroids of any size locked into a stable orbit.
The status of moons could change if their primary's classification changed. For example, Miranda was a moon of the gas giant Burnham. When Burnham was helioformed, Miranda was reclassified as a planet. Miranda's moon, Caliban, remained a moon under both conditions.
Most moons that underwent terraforming did so at the same time their primary was being terraformed. Some moons required further development and were still terraforming while their primaries and neighboring moons supported large populations.
The Verse had approximately 122 terraformed moons, two of which (Priam and Zephyr) were technically part of double-planet systems but retained their original "moon" classifications. Approximately 25 moons were still undergoing terraforming. Twenty-two planets were once moons and later reclassified due to helioforming, and 32 moons were eligible for reclassification should their gas giant primaries ever be helioformed.
The smallest known moon was Bullet (of Hera) with a diameter of 125 kilometers. The smallest inhabited moon was Ita (of Whittier, with a diameter of 965 km. Despite the massive populations of the Central Planets, it was the moon Conrad (of Three Hills) that claimed the highest population density in the Verse.