that's about the equivalent of calling someone 'asiatic', a term used for animal species lmao. of course you probably don't give a shit, and neither do we really care about calling you names either.
It's gone out of favor in the US (because people like to change every term with newer versions) but it's still a word just meaning "being from asia".
It's both, but as an ethnicity it's subdivided in several cases based on their origin (e.g. "white mexican").
But can also be seen as the future/aspiring all-encompassing Mexican ethnicity through the inter-mixing (cultural and genetical) going on for centuries...
(It's not like "Spanish" in Spain are some pure ethnicity that always existed either, it's one that emerged by combination of several ethnicities).