Well, at least with the English-speaking context I’m familiar with, we never really call European countries who speak Romance/Latin languages “latinos”. We call them perhaps “Romance/Latin-speaking countries”. Kind of how we usually don’t call countries with Germanic languages “Germans”? We might say Germanic-speaking nations.
From my own experience, I’ve always heard “latin@” being used to refer to people from Latin America, not to Europeans in Latin-speaking nations. The notion I get is that it’s simply meant to denote the linguistic and cultural difference from British North America, by therefore grouping all the former Spanish and Portuguese colonies together, Spain and Portugal both being culturally more similar as neighbours on the Iberian peninsular. Technically Canada has French influence too, but the sense I get is the crucial distinction being made is between British influence/Spanish + Portuguese influence. Hence the terms “Hispanic” or “Latino”- because of the extensive Spanish and Portuguese cultural influence over the Americas, plus the fact that people in Latin America are a mix of ethnicities due to immigration and colonisation.
I get the sense this collective term is used because things like a geographic demarcation such as “North America” aren’t adequate as Mexico is part of North America, and had Spanish influence. It wants to group the cultural entity imo. But again, usage of this term is not exactly consistent- I have personally not really heard of Filipinos being referred to as “Hispanics” even though like Mexico, they were a Spanish colony for like 300 years and absorbed a lot of Spanish influences- lots of surnames and given names are Spanish.
But I suppose in other places the terms may be used differently, which is why you learnt otherwise- it all depends.