It seems from my research that the Peloponnesian League asserted it's dominance through hegemony. If you read the context of how Sparta maintained alliances it's clear that it was a one way street with each ally. Since there is not apparent a sense of unity that grows from mutual collaboration between states it might make sense to view these as separate identities.

Of course from an external viewpoint of the Persians for instance, you might see more of a "they are all Greek" perspective. But you also need to realize that political strategy and cunning is nothing new. Xerxes strategy was to help sponsor different tyrants in various city states to help foster infighting. Tom Holland is an author that is cited often for instance Persian Fire: The First World Empire and the Battle for the West.

The parallel exists between the kind of puppet states or factions we have in hotspots today, those same problems affected the Persians as they attempted to sponsor one faction against each other.

It would be nice to here from some experts on the matter.