Zeus, father of Apollon and king of the gods, has quite a large number of epithets, and quite a few of these are shared with his son. If you worship either Zeus or Apollon under any of these epithets or are curious about them and would like to do more research, I encourage you to submit a piece (prose, poetry, prayer, art, and academic papers are all encouraged!) to the devotional.
Άγήτωρ (Agétor) means leader and ruler. It is perhaps more obvious why this epithet belongs to Zeus than why it belongs to Apollon, but we should remember that Apollon, in his oracles, speaks the law of Zeus.
Άγώνιος (Agónios) means helper in struggles or who helps in contests, or maybe just of contests. Translating epithets has certainly turned out to be tricky business. This epithet actually also belongs to Hermes, for obvious reasons, but seeing as how Zeus and Apollon also had ancient games (the Olympics, the Pythian Games) held in their honor, it makes sense to call on them for help as well. Perhaps you can find other connections?
Άγοραιος (Agoraios) means god of the agora. The agora is the open public space used for assemblies and markets, so quite a few gods have this epithet.
Άλεξίκακος (Alexíkakos) has been translated in quite a few ways that all mean very similar things – he who wards off evil, restrainer of evil, he who diverts calamity, averter of evil, and then also plague healer. Apollon was given this epithet by the Athenians because he stopped a plague during the Peloponnesian War. What about Zeus? Care to dig into it?
Καταιβάτης (Kataibátes) is another epithet with quite a few translations, some similar and some not. I have seen it translated as he who grants a happy return home (from war or abroad), who comes down, who leads down, and he who descends. In Zeus’s case, this epithet often refers to his thunder and lightning, which descends from the heavens, and he had an altar under this epithet at Olympia. What do you think it means for Apollon? Apollon and Zeus also share this epithet with Hermes – would you like to find the connection between all three?
Καθάρσιος (Kathársios) means the purifier but has also been translated as the atoner. Apollon is well-known as a god of purification, and Zeus had a temple under this epithet in Olympia.
Κλάριος (Klarios) has been translated in some very different ways that are actually related. I have seen both supervisor over cities and colonies and distributing by lots or of lots. The last one is probably the most accurate, but as a κλάρος is an allotment of land, you can see where the connection came from. For Apollon, this has often been connected to both his roles as an oracular god and as a god of colonists. According to Pausanius, a hill near Tegea was sacred to Zeus Klarios.
Λύκειος (Lykeios) is an epithet whose meaning is hotly contested. The translations vary from of the wolf, wolf-slayer, protector from wolves, wolf god, deliverer from wolves, and of wolves to of the light, light bringer, giver of light, and born of light to destroyer to born in Lycia. It is from this epithet that Apollon gets his association with wolves, but as he is also the preeminent god of light, that association is also clear. As for Lycia, well, Delos isn’t in Lycia, but there are some who say that Leto came from there, and some argue that even though many call Apollon the most Greek of gods, that he was actually originally a foreign god who came to Greece by way of Turkey. In Zeus’s case, this epithet is a little clearer yet wholly different. It refers to his worship on Mt. Lycaeum in Arcadia. Zeus and Apollo also share this epithet with Pan (who has his own reasons for it). Care to weigh in on the mystery?
Μοιραγέτης (Moiragétes) has been translated as leader of the moiroi (meaning ruler of fate) and guide of the moirae. For Apollon, this was one of his epithets at Delphi, where he shares the will of Zeus.
Πατρώος (Patroios) has multiple translations, but they pretty much all mean the same thing (in context) – he of the ancestors, father, protector of families, protector of the Ionians, and ancestral. This epithet is used for any god to whom the people trace lineage or whose worship has been handed down from their ancestors. Zeus was an ancestor god in Athens and in any area where the kings descended from Heracles.
Φυξιος (Phyxius) means protector of fugitives. It was an epithet of Zeus in Thessaly.
Σώτερ (Sóter) means savior. It was used for Zeus in several places, and in addition to Apollon, it was also used for Helios and Dionysos.
Χρυσάορος (Khrysàoros) means with sword of gold or wearer of the golden sword. Zeus had a temple under this epithet in Caria, and this epithet was shared not just with Apollon but also with Artemis and Demeter. Many people don’t think of or perhaps easily forget that Apollon has a golden sword (and a golden bow as well as a silver one). Would anyone be interested in working on the connections between this epithet and any of these deities and Apollon?