Accuracy vs. Precision
But, they're the same thing, right? Not exactly (Eli, is that your idea of a joke?. . . more or less.) You can only build as accurately as the tolerances of your measuring and marking tools will permit. For the overwhelming majority of tasks, careful use of the usual critters is quite sufficient. However, there inevitably arise situations where you need more precision than that.
For example, to encourage my work to come out square, my best practice was to cut all the parts that wanted the same dimension; from the same fence setting or saw stop - at the same time. A case where “the same” has greater precision than the most highly accurate repeated measurement. Much faster too.
Another example is, when making measurements to mark out cuts for interior parts, using scrap stock of the actual exterior parts rather than relying on measurement or calculation.
More pointed examples include:
When the size of the object is beyond the margin of error of your square
If your framing square is 1/8 deg out of true that's a 1/2” error at 20'
Where the calculation of a distance or a division is cumbersome or will produce an unmeasurable number
39-5/16” into seven equal parts
When you must lay out all, or part of a large regular polygon that isn't rectangular
Where you require an ellipse or elliptical arc.
When you must fit together objects too large to be worked on the available bench tools.