Interesting hybrid for your first place-name! Saint Martin is half an island and a part of France; the other half of that island is Dutch-speaking Sint Maarten. Research the first three to see why they are indeed countries. Grenada is between St Vincent and Trinidad.
Exactly. It is a part of the country of the Netherlands (the remaining part of which is in Europe). Sint Maarten, Aruba and Curaçao are three of the four countries that comprise the Kingdom of the Netherlands, alongside the country of the Netherlands.