The ways that Ancient Greek city-states were different from modern US states include;
Ancient Greek states did not have a single central government that united them like the federal government of the United States unites the states. Eventually however, they developed a central government when the armies of Philip II of Macedon conquered most of Greece and took it over.
The U.S. states are also run by people who were elected to their positions unlike the Greek City-States who were often run by Kings such as Sparta and Thebes. This wasn't the case in all Greek City-States as city-states like Athens, Chios and Thebes practiced democracy. But, most city-states like Sparta and Macedon were kingdoms.
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