Two planets are exactly a hundred and twenty degrees apart perhaps once in a chart. Everything else is approximate, and the amount of approximation an astrologer will accept is called the orb. There is no agreed figure, there never has been, and the disagreement is not a detail: it decides which aspects appear in a chart at all.
The traditional answer gives the orb to the planet. In Lilly's Christian Astrology of 1647, and in the medieval Arabic-derived material behind it, each planet carries its own radius of influence, its orb, sometimes called its light or its beams. Lilly's figures run to roughly fifteen or seventeen degrees for the Sun, twelve for the Moon, nine or ten for Jupiter and Saturn, and seven or eight for Mercury, Venus and Mars. Two planets are in aspect when the distance between them falls within the sum of their moieties, each moiety being half that planet's orb. The consequence is that an aspect involving the Sun reaches much further than one between Mercury and Venus, and the same angular separation counts as an aspect in one pairing and not in another.
The modern answer gives the orb to the aspect. Twentieth-century practice mostly abandoned moieties and assigned a fixed allowance per figure: something like eight to ten degrees for conjunctions and oppositions, six to eight for trines and squares, four to six for sextiles, and two or less for anything minor. Which planets are involved becomes at most a modifier, usually a widening for the Sun and Moon.
Neither scheme is derived from anything. Both are conventions, and the numbers vary from author to author within each. Astrological software makes this invisible by shipping a default orb table and drawing the aspect lines accordingly, so two astrologers looking at the same chart in two programs are looking at different charts. Where a reading here depends on an aspect being present, it is worth knowing that the aspect's existence is a setting.