The difference is that U.S. passports don't distinguish which state you are a citizen of. Hawaii does not have its own representative in the United Nations. Hawaii does not have its own ambassadors and consulates. EU passports do distinguish which country you are a citizen of. Each EU country has its own representative in the U.N. and its own ambassadors and consulates [1].

Free travel is not the feature that is legally indicative of a nation.

[1] Yes, I know that EU consulates can be shared by other EU citizens. Nonetheless, legally there is no such thing as "an EU consulate" or "an ambassador from the EU" or a generic EU passport. It really is a radically different model from the EU. (The most notable difference is that countries can unilaterally withdraw from the EU without triggering a civil war within the EU. States can't.)