I don't know who Apollon Olympia was. Apollon Olympios was one of the appellations given to Apollo, in Greek Απόλλων, or Apóllōn . The gods had various manifestations, or avatars, if you will accept that word loosely, each manifestation had a distinct appellation. No matter what manifestation a god was called he was still all the manifestations at the same time. It makes the Holy Trinity look easy. Apollo has a lot of appellations, or nick names, if you'll also allow that, one is Apollon Phoebus for Apollo in the context of the sun, which may explain the large number of other appellations. The sun has always been extra important, even today some of the most fundamentalist of protestant Christians make a big deal out of sun rise Easter services. Apollon Alexikakos is Apollo the healer, sworn by in the classic Hippocratic oath. Apollo Loxias ("the obscure"), is Apollo as god of prophecy , Apollo Delphinios, is Apollo of Delphi, and Apollo Pythios is Apollo actually AT Delphi. ( He was always there but he wasn't always there, he was a randy god and was always, but not always, off chasing women and men) Olympios has at least four meanings when appellated to Apollo. (Here it might behoove you to think about the differences and similarities of "as" "of" and "at.") Olympios is applied to the major gods and goddesses, the ones that actually lived on Mount Olympus and "controlled" the mortal world, Apollon Phoebus , as god of the sun, though Helios was the real god of the sun and the people who called Apollo "Phoebus" knew that, qualified as one of them. If you wanted help for a disease you prayed to Apollo Alexikakos, if you needed big time help you sacrificed to Apollon Olympios, he was the sun and son of Zeus after all . Mt. Olympus was a real mountain right there on the outskirts of Athens and the gods really did live right there on the mountain, but every and all Athenian could go up there and try to find them and they would never find the home of the gods. It wasn't like another dimension, it was right there in front of them. but most of them just couldn't find it. So the Athenians built temples to the gods up there . One of the Apollon Olympios was him residing in the statue and temple on the material mountain,and he really was there, the statue wasn't a visual aid, the god was the statue and the statue was the god, but the statue wasn't the god, it was the god, understandable to mortal men, but not the one that lived in the god's Olympus ( Which is why it is so hard to determine what the definition of idolatry is . Now, Apollo got tossed out of the god's Olympia for nine years, he killed Python, son of Gaia ( the Earth) But god time and man time don't necessarily coincide. You could pray to Apollo after he came back to Olympia ( a prayer of penance) or the next day you could pray to him before he was exiled when he was still the glorious sun. Apollo, after he is allowed back in, is also appellated Apollon Olympios, the god of penance. Now we finally get to what you , as a "modern" western hume bean wantta know about "Apollon Olympia, " Apollon Olympios can be translated as Apollo of the Olympics. The Olympics was a sacred festival with prayer sessions, sacrifices, and other ceremonies dedicated to the gods of Olympus ( remember them, the primary gods including Apollo?) There were some athletic contests involved with that inspired our modern purely athletic contests.( There were also some debating, theological debates and dramatic contests that maybe became the Academy Awards, but who am I to compare contemporary society to that of the classical Greeks ?) The Olympic religious services were started with a prayer to Apollo of, in,as, or at the Olympics ( Apollon Olympios) to light a fire in his guise as Apollo of, in, as or at the sun. ( Apollon Phoebus) Nobody knows if they used a lens or a parabolic mirror for Apollo to look through and start the fire. In modern times we have used both. And that is all I can tell you about "Apollon Olympios" unless you want me to get verbose and tell you about a bunch a stuff you didn't ask about.