Mexicans are Americans
Mexico is in the continent/s of America, therefore Mexicans are Americans. Not by nationality, but by mere geography. The same is true for Brazilians, Canadians, etc.
It might interest you to learn that Alexander Hamilton who wrote some of the Federalist Papers, used American in both senses of the word (continent/s and nation).
Also, United States of America was then thought of as a Union of independent States, America being the geographical location. Thus, you could be a Virginian or a Bostonian. The Spanish colonies were also American colonies, but they did not belong to the United States of America.
Why does this matter? First of all, if you want to visit another country in the Americas, you may want to avoid standing-out and coming across as ignorant; second, many Latinoamericans are proud of their shared identity, and it can be offensive to use American to separate them from this identity.
Finally, the slippage between American (country) and American (continent) is often used to justify “American Exceptionalism” when politically convenient.