As stupid as it may sound, I can't figure out the differences between them, it looks like Karnak itself was mainly a walled complex to the north of Luxor, which seemed to be a walled city with a temple in the middle, all on the eastern bank of the Nile. But even if all of that is correct, is Thebes just another name for Karnak? Sorry for the confusing question, I'm really confused as well and need to get all of this straightened out for a project I'm working on. I want to get familiar with the area (as familiar as possible without going there) but I'm having quite a bit of trouble with that.
Karnak is built on the Western side of the Nile, and is essentially a temple complex for the dead. Historically, the Western side has been reserved for death, while the land area East of the Nile has been a place for the living. The Giza pyramids are on the Western side, as is the Valley of the Kings. Memphis is a tad strange in this regard since nowadays the city is located on the Western side. However, that is because the Nile has shifted it's course - the city was originally located on an island in the middle of the Nile.
Anyway, as for the other two, Luxor was a religious site mainly used during the 18th dynasty (and relevant to you, restored by Alexander the Great). It's not a place where people specifically live, but a place dedicated to the worship of a god. Thebes was the capital of Egypt on and off during the course of it's 3000 year dynastical history, and if you look on a map, it's situated on the Eastern side of the Nile.
Does that make it clearer? In the late 3rd century the true purpose of these would obviously have changed a bit, but while the Greeks ruled Alexandria, the Egyptians would surely have known and followed the customs for the rest of the region.