Since Titan and Ganymede fall into the same category as Deimos and Phobos or the components of planetary rings, the category of moons, it's like if all asteroids were considered planets. Tiny irregular satellites are called 'moonlets' but still fall into the category of moons.
Is there any distinction between the natural satellites and should there be one? From my point of view, only equilibrium-shaped spherical moons should be considered moons. While natural satellites are all satellites, the spherical ones should be moons. Otherwise it would be extremely weird that Deimos and Phobos fall into the same category as our Moon or the Galilean Moons. For example, Pluto should be considered having five natural satellites, and one of them (Charon) is a moon.