Yeah this ball is incredibly shiny compared to the moon which is mostly made up of rock with something like 18% reflectivity.

But its not only that, this is a great showcase between the differences of a point light and something like the sun.

Simple setup I did in blender.

https://ibb.co/yBZgh8NX

A simple sphere with a moon texture and a bump map that I found on google. The sun is a unit back farther than the point light, because distance isnt really a factor with sunlight in a simulation. Both set to about the same intensity.

https://ibb.co/RkLCwmbS

The difference is striking. This has something to do with how far the sun is away, but I remember reading it has something to do with the size of the sun and its emitting light as a disc and not from a point, but cant find a reference to back this.

Which one looks more realistic though?

Hold two ends of a super stretchy rubber band. If a friend held the middle of the rubber band and stood a few inches in front of you, then the rubber band would make an angle and the ends would be clearly pointing away from your friend in different directions. If your friend took a few steps away, that angle will get more narrow. If your friend walked very far away, then the angle will go towards 0. And so the ends would be pointing away from your friend in almost the same direction.

The Sun is so far away that the light rays that reach Earth are almost parallel. You can see this effect when you look at the shadow of your hand near the ground and then you move your hand towards the Sun and see that the size of its shadow shouldn't change much. But if you do this with a light bulb in a room, your hand shadow will get bigger as it approaches the light.

Light is just so weird, behaving like a particle, and a wave.

Of course a simulation/program isnt how real light truly behaves, but just an approximation.