Some similar examples:

saying "Англия" (England) actually meaning "Великобритания" (Great Britain, the UK) which includes England, Scotland, Wales and Northern Ireland;
saying "Голландия" (Holland) actually meaning "Нидерланды" (the Netherlands), where North Holland and South Holland are just two of their 12 provinces (Netherlands - Wikipedia, the free encyclopedia);
eariler: saying "Россия" (Russia) actually meaning "Советский Союз, СССР" (the Soviet Union, the USSR) which used to consist of 15 union republics, Russia used to be one of them.

Although the analogy is not quigte accurate. "America" when referring to the US belongs to "the whole instead of a part" relationship.
My examples illustrate a different kind of relationship: "a part instead of the whole".