No. The European Council is a meeting of leaders of member states whereas the Council of the European Union is a legislature of the European Union, similar to the European Parliament. The Council of the European Union contains 27 national ministers, 1 per state.

-Council of the European Union .

Commission, Parliament, European Council, Council

The E.U. is run through seven institutions. These are the Council of the European Union, Court of Justice of the European Union, European Central Bank, European Commission, European Council, European Court of Auditors, and European Parliament.

Brussels or Luxembourg