I need to be enlightened on Mexican diplomatic history, but I believe that "Mexico" was used for centuries to refer to the same region (generally speaking) and people who use the formal designation Estados Unidos Mexicanos today. By contrast, USA was the first and only name taken by the USA when that country declared its independence from England.
In the newspapers around the Spanish-speaking world, the president of Mexico is the president of Mexico, not the president of the United States of Mexico. But the president of the USA is the president of the United States.
I do not disagree with you here.
The poster to whom I was responding made the point that, as America is part of the official name for the United States of America, it would seem logical that citizens of that country be called Americans as opposed to citizens of, say Mexico, which does not make any mention of America in its official name at all, and which in fact derives from the
Mexica a Nahua Aztec tribe who in the 14th Century had their capital at Mexico-Tenochtitlan, and from whence the Spaniards began to call that area Mexico.
One must also remember that, until 1810, Mexico formed the nucleus of what was actually officially known as
Nueva España, and was not even an independent entity until 1821.
To make matters more confusing, however, their "Declaration of Independence" of 1813 was officially called the
Acta Solemne de la Declaración de Independencia de la América Septentrional, or the Solemn Act of the Declaration of Independence of Northern America.
So that the resulting territory, which at the time included the territory extending as far north as the 42nd parallel was to be considered for a time by the Mexicans to be Northern America.
Interestingly, however, when this newly independent nation finally achieved independence and recognition, it did so under the name of the Mexican Empire, and not the Northern American Empire, thereby demonstrating the preference for the Mexican rather than American identity.
This was followed soon after by the First Republic of Mexico, and so on. So that the Mexicans have never as a people identified themselves as American in any way other than an official, but only briefly used term to name their new entity in the Declaration of Independence in 1813. Since Spain never recognised the independence of this entity, but did later recognise the independence of the Itúrbide Empire in 1821, it was never technically a recognised term.