Red - Aldenard
Green - Ilsabard
Blue - Othard (you have to look really closely but you can see the edge of the continent there.)
Purple - Thavnair
Orange - Meracydia
Pink - The New World
The small city-state of Garlemald is located in Ilsabard, but the Garlean Empire controls all of Ilsabard and Othard since the Year 1552 of the Sixth Astral Era.
And yes, the Three Great Continents (Aldenard, Ilsabard, and Othard) are connected by land bridges which are visible on this World Map as well as the Eorzean Map. Aldenard has always been speculated as being the smallest continent, so I believe the term "Great Continent" refers to the fact that these three "great" continents are great because they are connected - a super continent if you will.
Hope this helps clarify things! ^^ Lemme know if you have more questions!