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This explains it very well: https://moon.nasa.gov/moon-in-motion/earth-and-tides/tidal-locking/
So why doesn't the moon rotate around the axis that's on the line that points from the Earth to the moon? The "Z" axis as we look into the sky?
Or does it?
Try recreating that spin with a fidget spinner and slowly turn it around like the moon turns to face earth. You'll find that it wants to turn in a way where it spins around the same axis it's orbiting.
Since the moon has no hand preventing it from doing that, it aligns its spin with the orbit, so the forces described in the article bring that rotation to a halt.
Pretty much everything in the primordial solar system orbited in the same direction and the same plane, and that motion is conserved to this day, for the most part. The moon would have had to have been captured for its rotational energy to be that different from that of earth's.
Looking into the sky isn't the z axis. It's more like r from polar coordinates. Z in Cartesian coordinates goes through the polls of the moon and earth roughly.
From our point of view. Interpreting our field of view as the grid.
In that case the grid changes as you move on the surface of the earth. "Up" is relative to the center of the earth and is not the same direction in any two places. Cartesian coordinates (the usual x,y,z people think of with graphs) is difficult to use in this case.
I'm talking about staying in one spot.
The axis that the moon and earth rotate around is close to parallel. However, this axis is almost never directly "up" unless you are near the rotational poll. To visualize where this axis would be, you can look at the star Polaris or the northern star (check out a star finder app). To get a better sense of what is going on, perhaps look at a time lapse that shows how the stars move around Polaris.