Chronos, time, and Cronus, the Titan who mutilated his father and swallowed his children, are two names with two spellings and two stories. Antiquity ran them together anyway. The identification was available to Hellenistic allegorists, for whom a god who devours his own offspring is an obvious figure for time consuming what it produces, and Roman writers repeat it; Cicero records the derivation approvingly in De Natura Deorum.
Because Rome identified Cronus with Saturn, the merged figure passed into Latin, and then into the medieval and Renaissance handbooks, as Saturn, and the attributes travelled with him. The sickle the Titan used against his father became the scythe of the reaper. Old age, the slowest of the planets, the melancholic temperament, agriculture, lead and endings all attached themselves to the same figure, and astrology inherited the whole bundle.
The winged old man with an hourglass and a scythe who appears in Renaissance and Baroque painting, and who still stands beside the infant new year in Victorian cartoons, is the end of that process. Father Time is not a survival of a Greek cult of Chronos. He is a composite assembled by scholars and painters out of a confusion of names. The atlas holds Chronos and Cronus as separate entries because the sources do distinguish them, whatever later usage made of the pair, and because the primordial Time of the Orphic accounts has a role in cosmogony that the Titan never had.