I live in latam but I am not mestizo or amerindian lol. Latino is not a race (neither is hispanic for that matter).
I know the US uses that terminology to lump all Latin American immigrants that aren't pure bred together but it is absolutely not helpful.
Latino: Short for Latinoamericano (Latin American), born and raised south of the US border, speaks a romance language (Spanish, Portuguese, French), it does not denote race, only ethnicity.
Hispanic: Speaks Spanish and is from the Hispanic diaspora, this includes actual Spanish people from Europe.