At the federal level of the E.U., the European Council, like the Senate in the U.S., represents the states, whereas the European Parliament, like the U.S. House of Representatives, represents citizens—that’s right, E.U. citizens. The theory behind this difference is a modification of traditional federalism theory, wherein only the polities in a federation are represented at the federal level. In this traditional way of doing federalism, individuals, or citizens, belong only to the first level of political organization. Althusius’s Political Digest (1603) describes that theory, borrowing a lot from the example of the Holy Roman Empire. The advent of both polities and federal citizens being directly represented at a federal level was born out of compromise during the American Constitutional Convention in 1787. The E.U. replicated the structure, wherein the state governments and E.U. citizens (or legal residents) each have their own channel of access to affect federal law and policy on the federal level. For one of the two to cross over and eclipse the other in its own channel is suboptimal because both vantage points contribute to sound federal law in a way that enables them to protect their respective interests, which are not identical. It is thus not appropriate for a state government, including its governor or head of state, to direct members of Parliament how to vote on a given bill, whether their districts are within or outside of the state.
The full essay is at "Meloni: Differentiate the European Council and Parliament."