My area of expertise lies within the European Union's institutions, so I'll discuss the differences between Council of the European Union and the European Council and why each body exists, drawing largely from Ludger Kuhnhardt's European Union: The Second Founding (2nd Revised Edition, Baden-Baden, Nomos Verlaggesellschaft 2010), which I find to be a comprehensive overview of the constitutional evolution of the EU, and the Treaty on European Union (Luxembourg, Publications Office of the European Union, 2010) for information on the responsibilities and powers of the institutions themselves.
The Basics of Each Institution
To start, the Council of Europe is separate from the Council of the European Union and the European Council. The Council of Europe is an intergovernmental organization with 47 members within Europe: all countries on the European continent except Belarus, Kazakhstan, and the Vatican. The Council of the European Union and the European Council, along with the European Commission, the European Parliament, the Court of Justice of the European Union, the European Central Bank, and the Court of Auditors, are institutions of the European Union, which has 27 member-states.
The Council of the European Union (referred to in the Treaty on European Union as "The Council") was established with the European Union in 1993 with the ratification of the Maastricht Treaty. The Council, as set out in Article 16 of the Treaty on European Union has both a legislative role (alongside the European Parliament, the Council votes on legislation proposed by the European Commission) and a policymaking and agenda-setting role (the rotating presidency of the Council establishes different priorities for each six-month term). The Council consists of a representative of each EU member-state at the ministerial level and its presidency rotates between member-states (Portugal currently holds the presidency). The Council has its roots in the three supranational bodies within the European Communities (EC): the European Coal and Steel Community, the European Economic Community, and the European Atomic Energy Community, or EURATOM. Each organization had a similar institutional structure, including a Council of Ministers, comprised of government ministers from each member-state.
In many ways, the European Council is an outgrowth of the Council of the European Union and its predecessor institutions in the EC. Today, the European Council is the newest institution of the European Union, having been formalized in the Lisbon Treaty in 2009. Article 15(1) of the Treaty on European Union charges the European Council with providing "the Union with the necessary impetus for its development and [defining]... the general political directions and priorities thereof." It is comprised of the heads of state or government of the EU's member states, its own president (currently Charles Michel), and the President of the European Commission (currently Ursula von der Leyen). The European Council meets rather infrequently --twice every three months-- and in special meetings when required, and when you hear about late-night summits in Brussels involving the different Presidents and Prime Ministers of EU member states, those are meetings of the European Council.
From Informal Summit to European Institution
The European Council's origins go back to 1974, though, when French President Valery Giscard d'Estaing convened a summit of the heads of state and government of EC member-states in Paris. The member-states would later agree to hold regular meetings, first three times a year, then two, then four, in accordance with the rotating EC presidency. The European Council's meetings were, at this point, conducted outside of the Rome Treaties, so decisions taken at these summits had no effect within the EC's legal structure. That said, the European Council did take important decisions in the late '70s: in 1978, the European Council decided to adopt the European Monetary System, an important step towards the adoption of the Euro. Under the Single European Act, the European Council would be given recognition in the EC's legal structure, but would not become its own institution, separate from the Council of the European Union until 2009. In many ways, in order to understand the European Council and why it exists today, you have to understand the move towards a European Constitution.
The move towards becoming a separate institution can be described as a process of Europeanization and constitutionalization. The Maastricht Treaty, which established the European Union serves as a useful demarcation line between the two forces. While increased federalism, economic integration, and a common market had been on the agenda since the early days of the EC, events of the early 1970s exposed the need for further cooperation and harmonization. The 1973 Yom Kippur War and subsequent OPEC blockade and the collapse of the Bretton Woods system exposed large differences within the member-states’ economic systems. The signing of the New Atlantic Charter in Ottawa in 1973 reinforced a feeling of European dependency on the United States. As the ‘70s progressed into the ‘80s, the rise of the “Asian Tiger” economies coupled with a general economic downturn in Europe threatened European economic competitiveness. Kuhnhardt (167-168) identifies four “robust and sustainable” European interests that emerge during this time:
It is in point 3 where we can see the roots of the European Council germinate. The growth of the EC up until the 1970s saw the Commission struggle in its role and the Council and the European Parliament struggle to balance the representation of the interests of the member-states on one hand with the representation of the interests of EC citizens on the other. Giscard d’Estaing’s decision to establish regular summit meetings was one of the first steps to ensure the EC could act decisively in light of those four European interests. In 1987, the Single European Act took effect, incorporating the European Council into the legal structure of the EC, but its function and form remained undefined. The Single European Act also charged the EC with realizing a single market by 1993, paving the way for the Maastricht Treaty and the establishment of the European Union.
At the same time negotiations in Maastricht began, new challenges began to present themselves in Europe: enlargement and expansion in Central and Eastern Europe behind the old Iron Curtain, Europe finding its place in a post-Cold War world order, and the belief that the EC and its institutions suffered from a “democratic deficit.” While the Maastricht Treaty established three pillars within the European Union (the Common Market, Foreign Policy, and Justice and Home Affairs policy) and strengthened the EU’s institutions, we begin to see the emergence of constitutional questions in the 1990s. Among those questions is one that seems simple at first, but is actually vital: who speaks for Europe. Additionally, the institutional, legal, and policymaking structures of the EU and the EC were highly opaque and complicated. It is in light of these questions we see multiple treaty revisions post-Maastricht, first in Amsterdam in 1997 and then in Nice in 2000. In December 2001, the European Council met in Laeken, Belgium and issued the Laeken Declaration, which defined several mandates for reform and called for a European Constitutional Convention, to draft a true constitutional treaty for the EU.
I won’t go into great detail about the European Constitutional Convention and the resultant Constitutional Treaty, since doing so would run afoul of the 20-Year-Rule. Voters in France and the Netherlands rejected the Constitutional Treaty in referenda, and treaty was abandoned. Two years later, the EU began the process of drafting a new quasi-constitutional treaty, which we now know as the Treaty of Lisbon. The Treaty of Lisbon established many of the things the Constitutional Treaty set out to do, while removing many of the constitutional and state-like features of the Constitutional Treaty. Among the provisions of the Treaty of Lisbon were articles that established the European Council as a full institution of the EU, with a permanent President, who can serve two two-and-a-half year terms. The President of the European Council is also responsible (alongside the High Representative of the Union for Foreign Affairs and Security Policy, essentially the EU’s Foreign Minister).