How are the Carribean Islands divided?

The Caribbean Basin is often divided into the Greater Antilles and the Lesser Antilles (the bigger islands and the smaller islands, respectively). The Greater Antilles includes the four large islands of Cuba, Jamaica, Hispaniola, and Puerto Rico. The Lesser Antilles are in the eastern and southern region.

Can you give an example of smaller Antilles even not connected to Carribean?

Examples are: Antigua, Tobago, Saint Vincent, Nevis, Saint Martin among others.