Okay, this whole debate is over the Moon being just reflected sunlight, right? And thus somehow connected to Sun Magic?
Well, what if the Moon in this setting is like this giant magical prism that alters the light of the Sun into something else? Light is just electromagnetic radiation in normal physics, and altering the frequency of electromagnetic radiation can mean the difference between a Radio wave and a Microwave. Same basic stuff, but very different effects. So the Moon could easily be doing that with Sunlight. 'Altering the frequency' of the Sun magic into something completely different, Moon magic - as distinct from one another as a Gamma Ray and an X-Ray. And the difference between Sun magic and Star magic is that Sun magic comes from a single concentrated source (with very specific focused properties), while Star magic comes from the overall 'background radiation' of millions upon millions of diffuse magical sources that all together result in their own distinct effect. City lights vs Laser might be the metaphor here.
Obviously I'm heavily conflating real life physics with magic here, but my overall point is that it's not that absurd for magic to be a singular 'force' that can have different effects dependent on how that force is applied and in what concentrations or energy states. After all, that's literally how our universe operates and we're in no short supply of phenomena.