Ancient Greece was made up of many city-states (polis) including Thebes, Corinth, Delphi, Argos and Rhodes.
Citizens in Ancient Greece didn't consider themselves to be Greek, they considered themselves to come from their city-state; therefore:
Corinthians came from Corinth
Rhodians came from Rhodes
The two most important city-states of Ancient Greece were Athens and Sparta.
For more on Ancient Greece, check out our Ancient Greek Compendium page.