I have not figured out the exact, logical, mathematical, astrological etc. things about the three moons, and I don't plan to; it's not important, I don't know how and I don't find it interesting. Thus: it's magic!
Red Moon; Blood Moon, Leech Moon, Rage Moon
The full Red Moon is also sometimes referred to as Hunting Moon. It's a time of blood and murder wherever vampires tread; they are bound to the phases of this moon and go insane with lust for death and blood while it shines full. This only applies to the "main" night of the full moon, though some vampires have been reported to display moon madness on the other two nights as well.
Silver Moon; White Moon
The silver sister does not cause madness like the red sister, but it has qualities beyond the worldly ones. Werecreatures are, in some way, tied to the cycle of the Silver Moon and react badly to Her metal, as well.
Green Moon; Sickling Moon, Serpent Moon, Chaos Moon
The Green Moon does not shine emerald light; she shines eerie, sickly light, like a poisonous phosphoric fungus. Beware those who worship the Serpent Moon: they are the bringers of the chaos, distortion and perversion that She represents.