Greek is one of the few languages with a continuous written record from the second millennium before the common era to the present, and the atlas divides it into stages because a text in one is not a text in another. Ancient Greek covers the classical dialects, Koine the common language of the Hellenistic world and of the New Testament, Byzantine Greek the medieval literary and liturgical language of the eastern empire, and Modern Greek the stage from 1453 onward. The division is not merely academic housekeeping.
A manual written on Mount Athos around 1730 for painters of icons, giving the subjects, the postures, the inscriptions and the pigment recipes, is composed in the working Greek of its own century, and calling that language eighteenth century Greek names a date rather than a language: what it is, in the standard periodisation, is Modern Greek at an early point.
Modern Greek preserves a great deal of older morphology, so a reader trained on the classical language can often follow it, and the continuity is part of why the periods blur in ordinary usage. But the vocabulary, the syntax of the verb and the loss of the infinitive all separate it from what came before, and the church's own practice recognises the gap by continuing to serve in the older form.