Gods different from other superpowered beings

Awhile ago I was inspired to write a fantasy story about a war between gods. I brainstormed many characteristics and came up with a few scenarios.

In one of them there was a limit to how powerful a mortal magician could get. Their proficiency in magic casting could only get so good. Even the weakest gods had power far beyond that of a mortal, and they would only get moreso as they continued to live and grow (gods do not die of old age).

In another scenario, while wizards could get incredibly powerful, gods were infinitely awesome creatures. Imagine a fight between two tribes of master wizards in the middle of the wilderness. In a fantastical battle, they shoot bolts of lightning and summon mighty gargoyles to ravage their enemies.

Then a god appears.

Every man and monster stands in awe at the god (and any animals too, should they be nearby). Some go into a giggling fit, some drool on themselves, others cry a bit, but everyone's eyes are on this unknowable creature. They're stupified. They cannot think about anything but the god.

After the god leaves, everyone slowly breaks out of their figurative petrification but very few are unscathed. Most suffer from some form of mental devolution and a few even mutated physically.

Many works simply treat gods as a specific race of beings. So, a god is a god because they're a god. A wizard may be more powerful than a god, but the god is still a god. I've never been a huge fan of that approach, but it does simplify things.

In my Black series, faeries/demons are worshiped but are not gods; conversely, gods may go without worship for ages, yet they remain gods. If I could come up with another explanation, I would.