Divine Illumination is for gods; in fact, some of the strongest beings atop the stars are merely at the Divine Illumination Realm.
Above Hidden God is Heavenly Passage, this represents a breakthrough from the Hidden God Realm; all divine spirits and physical bodies are unified as one, able to be called half a god and, in a thought's span, can roam the starry skies.
Such level of power qualifies one as a minor expert in the cosmos.
Star-picking, as the name implies, means one can pluck stars with their hands and harness starlight for their own use, condensing the Divine Rules between heaven and earth. With every gesture and movement, these individuals wield infinite might, nearing the divine.
Divine Illumination embodies the universal shine of godly light, having transformed into a true divine spirit. Such mighty beings can command a domain of stars.
As for the realms of Heavenly God and Divine King, there are no detailed descriptions—perhaps the lady was unaware of these realms.