Dialect was probably the wrong word, because of course there’s many different dialects in many countries. (In fact, your aside about “sounds very US American” is funny, since I guarantee the US has more dialects than Spain. Plenty to hate on the US for, but that ain’t it.)

Anyway idk if there’s a word for this but like, the intermediary level between a language and a dialect. There is a wide gulf between Spanish spoken in Spain vs Latin America the same way as English in the UK vs USA. That macro-level distinction breaks down into trees of further distinction in regions, cities, towns of course.