I've done several shoots lit only by the full moon. Doing long exposure, the images are as you stated not much different than an image taken during the day, except for looking at the sky and seeing stars.

I've also done video shoots with the newer mirrorless cameras and fast lenses shooting wide open again lit with nothing but the full moon. It again looks daylight on the image. As a bit of BTS, I recorded a video of the screen on the camera showing what it was seeing, and then pulled away and reframed to show essentially the same shot as the camera but it's just solid black. One of those videos was fun as we caught a bit of lens flaring from the moon, and you can actually see the details of the surface of the moon in the reflection. It was one of those things I just never considered before as flares coming from lights or the sun are just void of detail.