In a federal system, the central (or federal) government has much more authority than in a confederal system. The central government controls more trade policy, and makes decisions about policy areas that involve interactions between states (such as highway systems).
Nationality is a legal relationship between an individual person and a state. Nationality affords the state jurisdiction over the person and affords the person the protection of the state. What these rights and duties are vary from state to state.
Nationality is the country you were born in, regardless of your citizenship. America is not a country. The United States of America is. So, your nationality is United States of America. Take your passport (if you don't have one, you've never travelled, then you shouldn't be giving advice on anything) open it up, and look under Nationality. It says United States of America.