The Council meets in different configurations, the list of which is adopted in accordance with Article 236 of the TFEU.

Today, the configurations are:

Of those configurations The TFEU mentions two - The General Affairs Council, and the Foreign Affairs Council:
The General Affairs Council shall ensure consistency in the work of the different Council configurations. It shall prepare and ensure the follow-up to meetings of the European Council, in liaison with the President of the European Council and the Commission.
The Foreign Affairs Council shall elaborate the Union’s external action on the basis of strategic guidelines laid down by the European Council and ensure that the Union’s action is consistent.

The Presidency of Council configurations, other than that of Foreign Affairs is held by Member State representatives in the Council on the basis of equal rotation, in accordance with the conditions established in accordance with Article 236 of the TFEU.

 

Excerpt of PROTOCOL (No 36) ON TRANSITIONAL PROVISIONS:

Until the entry into force of the decision referred to in the first subparagraph of Article 16(6) of the Treaty on European Union, the Council may meet in the configurations laid down in the second and third subparagraphs of that paragraph and in the other configurations on the list established by a decision of the General Affairs Council, acting by a simple majority".