To expand on that a bit, the moon is directly lit by the sun. A proper exposure for the moon is not different from any other scene brightly lit by the sun.

We often associate moon with night, and night with needing high ISO, long exposure and wide open aperture. And when you use the auto mode on camera's, that is indeed what you will get because even with telephoto lenses the moon is only a small part of the field of view, so the camera will base its exposure on the dark sky around the moon. That will case an overexposed moon, with a lack of contrast.

(Another issue you'll encounter trying the view or photograph the moon is that when viewed with large amplification, the moon is actually pretty fast and you're going to have to re-aim your camera regularly.)

Night mode uses image stacking, denoising, and HDRI to improve the image quality. It should make a difference here?