Always ask individual preference.
African American, Black
It’s acceptable to use these terms interchangeably to describe black people in the United States. When referring to a specific individual, use the term he or she prefers. Do not hyphenate “African American,” and lowercase “black.”
American Indian, Native American
These terms are synonymous. Some indigenous people in the United States prefer “American Indian” to “Native American.” It’s best to use individual preference, if known. When possible, use national affiliation rather than the generic “American Indian” or “Native American,” for example, Navajo, Hopi, Cherokee and so on. To specify someone who was born in the U.S. but isn’t Native American, use “native-born.”
Asian, Asian American
Use “Asian” when referring to anyone from Asia, but use “Asian American” (not hyphenated) when specifically referring to those of Asian ancestry who are American citizens.
Mexican American, Hispanic, Latino, Latina, Latinx
Use “Mexican” when referring to anyone of Mexican citizenship, and use “Mexican American” (not hyphenated) when referring to those of Mexican ancestry who are permanent residents or citizens of the United States. “Hispanic,” “Latino” and “Latina” are umbrella terms referring to a person whose ethnic origin is in a Spanish-speaking country, as well as residents or citizens of the United States with Latin American ancestry. The recently coined gender-neutral “Latinx” is not considered a standard word. You can use it in quotations, descriptions of people who request it and names of organizations, but always include a succinct explanation (for example, “the gender-neutral variant of Latino”).
In most cases, use “white” (lowercase). Don’t use “Caucasian” (capitalized) as a synonym for “white.” “Caucasian” and “Caucasoid” should only refer to the specific anthropological group they denote.