Before 1776, the colonies were called the American Colonies because they were colonies in the region of America. Sometimes called North American colonies. The America name referred to the continent of North America, which also includes Canada and central America. There's no comparison as an example but imagine if Phillipines and Indonesia renamed themselves the Unified Islands of Asia. That doesn't mean they are all of Asia because Asia is a much larger region than then. Technically the region that Canada and Mexico resides in, and the Carribean and South America are all "The Americas". Because that's the name of the 2 continents...

BTW the name America comes from Italian explorer, Amerigo Vespucci.