Continents are the biggest land masses on the planet Earth, surrounded by the oceans. There are six of them. (Seven if you count Europe and Asia as two different continents, which really they aren't if you think about it.)
North and South America have the same name and are connected but Geologically they are separate as they are on different Tectonic plate and are moving differently. South America and North America are jointly referred to as America.
(Columbus discovered America), or the Americas. Columbus didn't discover America, the people who lived there already knew those lands existed.)
Continents are larger than Islands, Australia or Antarctica are the smallest continents and Greenland is the largest island. So every land mass larger than Greenland is a continent and anything smaller than Antarctica or Australia is an island. If we ever discover intermediate land masses on Exoplanets we'll need better definitions.