As a white European, when I first found out about the separate Latino ethnic designation, I found it hard to get my head around it. In Europe, Latino people would either be classified by nationality, or as one of white/black/Indigenous American/mixed when discussing them in a racial context, based on their ancestry. I don't think the concept of being Latino as something separate from your nationality is well understood here. So no, it isn't just you. As I'm sure you're aware, race is a social construct, and it is interpreted differently all around the world, so ways of conceptualizing race from other countries are bound to seem strange if you haven't grown up with them! That's what I tell myself, anyway...

About the differences between Europeans: although we like to pretend that you can easily tell a white European's nationality from their looks, in reality, white Europeans are pretty homogenous. Once you take away markers like clothes, hairstyles, tans and body language, it is a lot harder to tell apart say a French person and a German than people like to believe. You can't really go by stereotypical colouring, either, because there are redheaded Spanish people, naturally blond Italians and dark Brits and Scandinavians. Basically, we Europeans would struggle to correctly guess a European nationality in many contexts, so we don't expect that you would be able to either!