The Peloponnesian Wars between Athens and Sparta happened after the Persian Wars. However wars between Greek city-states were not some departure from norms but rather "business as usual", perhaps interrupted by the unusually large alliance needed to the defeat the Persians. In this thread u/Iphikrates refutes the view that there was something unexpected about two Greek states turning on each other, and here he thoroughly explains the causes of the "First Peloponnesian War" when Athens and Sparta first became enemies. Some other answers that might interest you are this one about what aspects formed a common Greek identity despite their divisions, and this recent one goes into how the land of Greece was spread between the city-states, both by our good Iphikrates