America is not short for Middle America, it's short for The United States of America. There is no Middle America, and nobody uses that term except to refer to the central part and/or middle class of the United States. There is a Central America, which is the land connecting North America and South America. We are in North America. The reason everybody refers to the United States as America is because the only reasonable term to use for people who live in the United States is "American", so it makes sense to call the country "America" rather than "The United States", and since there is both a North America and a South America, people refer to them collectively as "The Americas", so there is no other "America" to be confused with.