As Memo has stated, geographically speaking Mexico is part of North America (remember NAFTA?)!
Continuing his observation, Costa Rica belongs to Central America, which is geographically delimited to include the countries of Guatemala, Belize, Honduras, El Salvador, Nicaragua, Costa Rica, and down to Panama. This is the "bridge" between North and South America!
South America "proper" starts with Colombia, and then Venezuela, Ecuador, Peru, Brazil, Argentina, Bolivia, Paraguay, Uruguay, Chile, Falkland Islands (UK), French Guiana (France), Guyana, South Georgia and South Sandwich Islands (UK), and Suriname.
All are hispanic (some countries are, of course, former colonies of Portugal, France and the UK) or Latin America, including Mexico, but with certain nuanced cultural differences. I think this was what the "Gringos" would call or refer to as "South of the border!"
But in speaking of the "Americas," this includes North (Canada, U.S.A, and Mexico), Central, and South America.
Take your pick!