While Americans can mean "from the US", the term "statunitensi" is how people from the US are commonly called in Italy. And in other countries. The two things are not mutually exclusive, and calling Americans for people from the US is just a figure of speech called synecdoche.
The United Provinces of the Río de la Plata (Spanish: Provincias Unidas del Río de la Plata), earlier known as the United Provinces of South America (Spanish: Provincias Unidas de Sudamérica), was a name adopted in 1816 by the Congress of Tucumán for the region of South America that declared independence in 1816, with the Sovereign Congress taking place in 1813, during the Argentine War of Independence (1810–1818) that began with the May Revolution in 1810. It originally comprised rebellious territories of the former Spanish Viceroyalty of the Río de la Plata dependencies and had Buenos Aires as its capital.
But then it clashes with the naming of other people that live in America. We south americans also call ourselves Americans because we live in América – taught as a single continent with two subcontinents. We call people from the US Estadounidenses because “Americans” wouldn’t make any sense for us.