"Latin America" refers to the Americas where Romance languages (derived from Latin) predominate. The linguistic map is straightforward:
18 sovereign countries + Puerto Rico (US territory): Argentina, Bolivia, Chile, Colombia, Costa Rica, Cuba, Dominican Republic, Ecuador, El Salvador, Guatemala, Honduras, Mexico, Nicaragua, Panama, Paraguay, Peru, Uruguay, Venezuela. (Equatorial Guinea in Africa also Spanish-speaking.)
Brazil — sole Portuguese-speaking country in the Americas; 215M people (half of South America’s population).
Haiti (co-official with Haitian Creole).
French Guiana (overseas department of France).
Guadeloupe, Martinique, Saint Barthélemy, Saint Martin, Saint Pierre & Miquelon (French territories).
Term coined 1850s (French: Amérique latine) to group Spanish/Portuguese/French colonies against "Anglo-Saxon" America. Linguistic, not geographic.