There is water on the moon! As we’ve outlined before, it’s somewhat tricky to keep water on the surface of the moon, because the combination of heat and particles from the Sun, a lack of an atmosphere, and no magnetic field means that it’s pretty hard to keep water that’s exposed to sunlight from evaporating away into space.
What that means is that if you want to have water persist anywhere on the Moon, it has to be sheltered from the Sun somehow. An easy way for this to happen is at the poles, where some craters are deep enough that the Sun’s rays never reach into the bottom of the crater. Places like this are called “cold traps”, because it can trap material in a solid form that would otherwise escape if it weren’t so cold.
Near the south pole of the Moon in particular, we found frost in some of these deep dark places. This frost makes the surface more reflective than it would be if there were only rock sitting around in those craters - so the coldest places also wind up being more reflective if you’re bouncing light off of ice. This particular study is careful to note that we’re not seeing frozen pond-style pools of water, but more like the frost that builds on the outer edges of leaves in fall.
But craters aren’t the only places that water ice could hide - we have a sneaking suspicion that the Moon also has tunnels woven under its surface. The Moon had a surprisingly long era of volcanic activity in its younger years, and where there are lava flows, you can wind up with lava tunnels. We are pretty sure that the moon has these. We see them most easily as they collapse, because then you get a snake-like pattern of collapsed ground, twisting its way across the surface as a series of giant potholes.
Every so often, there’s a more isolated cave-in, giving us a glimpse into a sublunar cavern - a deep shadow cast into the depths catches the eye and the imagination. If water had accumulated in these hidden tunnels, they would also be relatively protected from evaporation. However, it’s one thing to have a plausible place for water, and another to find it for sure in those places. Lava tunnels are an extremely appealing place for water, though - because they’re also an appealing place to put a human base on the Moon. While we don’t have to worry about humans evaporating, any shelter from intense heat and cold helps us as well. So if there were also water down there, they’d be a great place to put an inhabited base.
You can definitely also wind up with watery molecules bound up in the rocks themselves. A recent study suggests that instead of having lots of water ice hanging around, the Moon may have a lot of hydroxyl, which is one hydrogen and one oxygen bound to each other, rather than the two hydrogens and one oxygen that make up your standard water molecule. Hydroxyl binds easily to other things, so it can wind up binding itself to minerals in the earth - you can extract it and create water, but it’s more energy intensive than just having water lying around.
So the true answer is that there’s going to be a mixture of places where water will be found - on the surface in sheltered places, possibly in underground tunnels, and some not-quite water bound up in minerals!