South of the Rio Grande, they use the term "mestizo", which means somebody of mixed Caucasian and Indian ancestry. Most of Latin America is mestizo, with the wealthy classes being more Caucasian, and the poorer classes being more Indian
My understanding is that the entire concept of a Latino designation is so vague as to make it effectively irrelevant in any sort of meaningful sense. An extremely wide range of people, from wildly different backgrounds, publicly define themselves as Latino. Carmen Electra, as an example does, as do many people whom you might think of as 'white' or 'caucasian' if you were to pass them on the street. It appears to be a "if you want to call yourself Latino, go ahead" sort of designation.
Well... the term "Latino" is not only ambiguous but overall incorrect. People from Latin American can be of European, Amerindian, African, Asian and mixed ancestry. For instance, Argentinians tend to be mostly Spanish/Italian, while Dominicans happen to be mostly mulatto.
What about dropping the term Latino/Hispanic overall and start using, for example, "White" for Cubans of Spanish ancestry, "Black" for Blacks from Colombia, "Asian" for Peruvians of Japanese ancestry and "Mixed" for Mexicans of Spanish and Aztec heritage.