I don't want to be a bore but this'll probably bit a long.
'Mexican' is just a nationality. There are Mexicans of mostly or exclusively European/Spanish (who were themselves a diverse nation) ancestry, there are Mexicans who descend directly from native populations, there are Mexicans of African ancestry, Asian ancestry, Middle Eastern, etc, and of course, Mexicans who descend from two or more of these groups.
The difference between Latin America and Anglo Saxon/French America is that the Spanish settlers didn't bring their families to the New World with them. These explorers and conquistadores took indigenous women as wives and their mixed children (mestizos) quickly became the majority in many Latin countries1 .Whereas on the British colonies the interaction between settlers and Native Americans was much more limited.
The intermarriage system was complex enough that there was a caste system depending on what your parents were. The more European your blood was, the more privileges you had. Someone born in Spain was European, but someone who was born to Spanish parents in the New World was a criollo. There were mulattos, Spanish and African, Zambo, African and Indigenous, castizos, Spanish and Mestizo. And some other more obscure combinations.
This went on for centuries. The caste system was abandoned but some of the terms survived. By the time our countries were independent, most of the population was considered mestizo, or mixed.
There are some predominant groups, for example countries like Argentina, Chile and Brazil had more intense immigration waves from Europe during the 19th and 20th, so you see a greater percentage of 'white' people in the Southern Cone. The population of Bolivia for example is mostly indigenous, and the Caribbean mostly African.