Ninety degrees is a quarter of the circle, which is why the square belongs to the fourth harmonic and shares its family with the semi-square and the sesqui-quadrate. Where it differs from its relatives is in status: the square has been a major aspect in every system that has used aspects at all, while the eighth-harmonic angles were latecomers and remain optional.
The older way of finding a square is by sign. Signs of the same modality, cardinal with cardinal, fixed with fixed, mutable with mutable, stand three signs apart and are therefore in square to one another as whole signs, regardless of the exact degrees involved. This is why the modalities and the squares are the same fact stated twice. Degree-based practice narrows this: a square exists when the angular distance falls within an allowed orb of ninety degrees, and a planet at the beginning of a cardinal sign has no degree square to a planet at the end of the next cardinal sign, though both sit in squared signs. Charts read the two ways diverge most sharply here, because the square is the aspect people act on.
The rank of the square has also moved. Traditional sources treat it as straightforwardly harmful, one of the two aspects of enmity alongside the opposition, and pair it with the malefic planets. Twentieth century practice recast it as productive difficulty, the friction that makes a chart do something rather than merely be something. The angle did not change; the reading of what difficulty is for did. Both positions are still held, and a reader who does not say which one they are working from is reporting a conclusion without its premise.