Columbus actually “discovered” and explored the Caribbean islands if Hispaniola (Dominican Republic/Haiti) and Cuba.
Pedro Cabral, en route to India in 1500, was blown off course and encountered Brazil--so even if Columbus had never sailed, the Americas would not have remained unknown to Europeans much longer.
Of course John Cabot's voyage in 1497 was earlier than Cabral's, but I think Cabot only sailed because he knew of Columbus' discovery.
Which all are part of the geopolitical region known as "North America."
List of sovereign states in North America
Antigua and Barbuda, The Bahamas, Barbados, Belize, Canada, Costa Rica, Cuba, Dominica, Dominican Republic, El Salvador, Grenada, Guatemala, Haiti, Honduras, Jamaica, Mexico, Nicaragua, Panama, Saint Kitts and Nevis, Saint Lucia, Saint Vincent and the Grenadines, Trinidad and Tobago, and the United States