Of all the moons in our Solar System, only one, Titan, has an appreciable atmosphere. But even Titan is mostly made of rock and ice, which doesn’t constitute it as a ‘gas moon’. In contrast, planets like Jupiter and Saturn are made mostly of hydrogen, with the primordial gas making up 90 and 94 per cent of their respective compositions. This is the reason why they are regularly referred to as ‘gas planets’. The early Solar System contained lots of hydrogen, but because the gas is very light, only really large planets could hold on to it. Jupiter and Saturn began life as solid bodies and grew to about ten times the mass of Earth. At that point they were able to capture and hold onto the hydrogen that permeated the young Solar System.
However, because none of the moons in our solar neighbourhood grew to a great enough size, none of them managed to capture any hydrogen. Titan successfully captured some heavier gases, which have given this moon its atmosphere. However, similar moons such as Ganymede and Callisto do not have an atmosphere, even though the former is bigger than Titan, while Callisto is roughly the same size. The reasons why Ganymede and Callisto do not have atmospheres, though, are still unclear.