How do defined terms change a classification?

A definition states the requirements for belonging to a category. Classification means deciding which things meet those requirements. Changing the category being considered can change a classification even when the objects themselves remain exactly the same.

Here a polygon has one closed, simple outline made of at least three straight segments. Simple means that the outline does not cross itself. Triangle A and square B qualify. Circle C closes, but its outline is curved. Path D has straight segments, but it does not close. Each fails a different part of the full definition.

A quadrilateral is a polygon with exactly four sides, so only B meets that narrower definition. The broader toy category closed outline allows curves, so A, B and C belong. These categories make different demands; selecting another term does not redraw any of the figures.

A useful sufficient condition is not always a complete definition. Being a triangle is enough to establish polygon membership here, but polygons also include B, so triangle does not define the whole category. Definitions also differ from empirical claims, which depend on observations of the world. Classifying these four drawings does not establish how common polygons are among signs in a town. That would require evidence about the signs, not just a definition.