The Punic Wars were a contest for supremacy in the Western Mediterranean between two rising powers.
The Persian War was a contest for supremacy in the Eastern Mediterranea.
They had nothing to do with each other.
The Punic Wars had no self or selves.
Carthage
Punic Wars established Rome as unchallenged in the Western Mediterranean, and their decision to punish Macedonia for supporting Carthage led them to progressively take over the eastern Mediterranean as well. The Persian, Peloponnesian Wars and Crusades did not involve Rome.
The Firdt, Second and Third Punic Wars.