Race in the context of physical differences does not map to the social concepts of race.
For example, US documents usually include Latino as a possible race, even though Latin Americans are white, black, indigenous Americans, or a mix - and Spaniards are what usually would be classified as white. If you check older forms you'd see Italians and Irish people categorized as a different (non white) category, etc.
You are correct. Most people who identify as Latino/Hispanic in the US consider that to be their race though, not ethnicity. So Census data has a lot of people who identify as Race: Other Ethnicity: Hispanic/Latino.
Race is distinct from Nationality. "Latino" is not a synonym for citizens of Latin American countries, but the name of a racial group which originated from that region of the world.
It gets confusing with countries like China, Japan, and India, which are more racially homogeneous, and where the country name is the same as the (common) name of the predominate racial groups.
The parent is talking about ethnicity (culture), not nationality. "Latino" isn't a race, it's an ethnicity. In particular, there are many "races" of people who are Latino (white Cubans, indigenous Mexicans, black Brazilians, etc can all be "Latino" despite different races and nationalities). Indeed the "latin" in "Latin America" and "Latino" was originally a language category--these peoples all spoke romance languages (Spanish, French, Portuguese, etc).
For example, US documents usually include Latino as a possible race, even though Latin Americans are white, black, indigenous Americans, or a mix - and Spaniards are what usually would be classified as white. If you check older forms you'd see Italians and Irish people categorized as a different (non white) category, etc.