Basically, any moving mechanical system has slop/clearance in it. When operating machine tools this is called “backlash”, aka how far you have to turn an adjustment handle before it creates a real change in machine position. Any and all moving mechanical systems will have some non-zero amount of slop.

Skilled operators can compensate and “take out” this backlash so that each cut runs perfectly true. Basically as long as you take a “sloppy” machine and always adjust it to run against the very edge of its “sloppiness” zone, you get high precision… I have used lathes at my old college with probably 0.100" or more of backlash and was still able to turn parts that had less than 0.001" of runout.

And obviously once you get to computer controlled machining centers the backlash compensation can be baked into the program to get perfectly true cuts each time.

Not OP, and I’m not sure how the lathe itself does it. But it shouldn’t be surprising that it’s possible to create more precise tools from less precise tools. Otherwise it would be impossible for us to ever create tools more precise than our own hands and fingers.

In terms of precision? Not entirely, there are limits to true mechanical precision that is necessitated by lubrication for moving parts, running fits, and natural vibrations.

When combined with other systems (aka computers) you are able to build shit like ASML microchip lithography machines…