Sparta.
A war is not a battle. The Persian War arose from Persia's attempt to stop war in the western part of its empire by bringing the constantly-warring Greek city-states to peace.
End
They were different - one was Persia versus a coalition of Greek city-states; the other was Greek city-states versus Greek city-states.
Independence, just as it was before the war. That is how the Greek world was structured.
Greek city states lose power at the peloponnesian war due to economic, infrastructural and agricultural ruin.
The Peloponnese war
The Greek city-states of Asia Minor revolted against Persian rule. This war spread to include mainland Greek city-states.
The Spartans were very focused on war. The boys after the age of 7, I think, were moved to camps where they were trained. Even the girls (the female gender was very underestimated in Ancient Greece) were trained because the Spartans supported that women's bodies had to be strong so that strong children were born from them.
Argos.
It was between an alliance of Greek city-states and the Persian Empire. Today we call it the Persian War to differentiate it from the wars between the Greek city-states. It is often called the Greco-Persian War.
The Greek city was in trouble because they had a long war with Romans. Look it says: "Almost 2,000 years ago, the people of Greece were in the middle of a long war with Romans."
The Persian thought the Persian Empire. The coalitions of Greek city-states thought the coalitions of Greek city-states.