Backlash, runout and the words for motion that should not be there
Every machine has movement it was not designed to have. The trades have separate names for each kind, and the name tells you where to look.
Unwanted motion is not one problem. It is a family of problems with distinct causes, and the vocabulary exists because the fix for each one is different. Using the wrong word sends the next person to the wrong part of the machine.
Backlash
Backlash is lost motion in a drive train. Reverse the direction of a leadscrew or a gear pair and the input moves for a moment before the output responds, because the clearance between mating surfaces has to be taken up first.
Some clearance is deliberate. Gear teeth need room for a film of lubricant and for thermal growth, so zero backlash is not the design target. The concern is change over time, since wear opens the clearance and the error grows.
Runout
Runout is different. It is the deviation of a rotating part from its intended axis, and it shows as a periodic error that repeats once per revolution. Where backlash appears only when direction reverses, runout is present continuously while the spindle turns.
Because the error is periodic, its signature is recognisable. A surface finish problem that repeats at spindle frequency points at runout. One that appears only at direction changes points at backlash.
Why the distinction pays
Backlash is compensated in software, taken up with preload, or removed by replacing worn components. Runout is corrected by fixing how the part is held, or by fixing the bearing or spindle itself. Compensating for the wrong one produces a machine that is worse in the other direction.