"Mexican" is a nationality, just like "Japanese", "French" or "Iraqi".
However when people talk about the ethnic groups they are referring to of course, the indigenous population. Namely Mexicas.
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All humans are of the same species. Race is a defined system and has no basis but what humans have assigned it. Scientifically, there is no such thing as different races of humans.
Hispanic is an ethnicity associated with people of Spanish or Portuguese decent. Commonly, these are people from the mid-Americas and Caribbean that are descendants of the Spanish conquerors that invaded these lands.