Presidency of the European Union

President of the European Union (or President of Europe) does not exist. Nevertheless, the term is often misused to mean any of:

Among the cases presented above, referring to the President of the European Council as the “President of the European Union” (EU) is very common in the international media. Nevertheless, this post presides only over the European Council – an institution of the EU – rather than presiding over the EU as a whole. The post does not have any executive powers and is unlike heads of state such as the President of the United States of America or the President of France: it is far more akin to or chairman. Letters of credentials for ambassadors of non-member countries to the European Union are presented to the President of the European Council.

The Commission Presidency has had fewer mentions using the term "President of the European Union", despite being the one with the most powers as the head of the executive branch of the European Union. The President of the European Commission is (loosely) analogous to the role of Head of a country's Civil Service (as opposed to the separate role of President of the European Council, who could be seen as the European Union's Head of State)

Prior to the Treaty of Lisbon, each member state (in turn) took the responsibilities of both the Presidency of the European Council and the Presidency of the Council of the European Union. The press frequently summarised these responsibilities to the shorthand tag "EU Presidency" or "EU President", both for the country holding it or its political leader. Nevertheless, this, too, was a misnomer.

There are other EU institution Presidents, but they do not hold the profile to have had the title applied to them.

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Wikipedia