Indeed, when people try to refer in English to the concept of "the American continent", they usually have to say "the Americas".

I think some people's Spanish has adopted this habit, saying e.g. "los pueblos de las Américas" or "las culturas de las Américas" more than "los pueblos americanos" or "las culturas americanas", but I don't have a broad enough exposure to Spanish to understand its prevalence and connotations clearly. (Maybe it's most common in the U.S. due to influence from English?)