The gods speak to each other, and bring things into being with a certain type of elemental magic called “Godspeak”. This is quite a lot more potent than regular magic woven by mortals. It can change the underlying rules of the world. It can create new races, it can keep islands floating in the air for centuries.
The Godspeak leaves a trace, which fades over time, which can be detected with for example detect magic, separate, or in addition to other schools of magic.
Lingering, undirected, leftovers of Godspeak, have widely unpredictable results. Maybe mutating the surroundings, maybe granting unconscious wishes of the people nearby, some high level magic users may be able to channeled leftovers to their own needs, or maybe loose Godspeak creates fields of anti-magic, death etc.
Demi-gods
Demi-gods are usually identified by them being able to wield a small piece of the Godspeak. At first only being able to cast a single spell using it or similar. But this may expand if their worship increases.