In American

United States

The United States of America is a federal constitutional republic comprising fifty states and a federal district...

 usage, a cotillion is a formal ball

Ball (dance)

A ball is a formal dance. The word 'ball' is derived from the Latin word "ballare", meaning 'to dance'; the term also derived into "bailar", which is the Spanish and Portuguese word for dance . In Catalan it is the same word, 'ball', for the dance event.Attendees wear evening attire, which is...

 and social gathering, often the venue for presenting débutante

Debutante

A débutante is a young lady from an aristocratic or upper class family who has reached the age of maturity, and as a new adult, is introduced to society at a formal "début" presentation. It should not be confused with a Debs...

s during the débutante season

Season (society)

The social season or Season has historically referred to the annual period when it is customary for members of the a social elite of society to hold debutante balls, dinner parties and large charity events...

 – usually May through December. Cotillions are also used as classes to teach social etiquette, respect and common morals for the younger ages with the possibility of leading up to a débutante ball.

This is similar to the Quinceañera

Quinceañera

Quinceañera , sometimes called "Fiesta de quince años", "Fiesta de Quinceañera", "Quince años" or simply "quince", is the celebration of a girl's fifteenth birthday in parts of Latin America and elsewhere in communities of immigrants from Latin America...

except for the ages.