Dragoons are, for the most part, only from Ishgard.

Most Dragoons are just using their own skills, the really fancy stuff is only usable by the Azure Dragoon, who gain power from Nidhogg himself via his Eye. I believe there is some implications that Midgarsomr helps power the WoL Azure Dragoon though?

All the skills you learn from the Job Quests are ones a normal Lancer can't learn. Some of them only an Azure Dragoon can use on top of that.

Dragoons as we know them first came about when King Thordan the First and his men fought Nidhogg. His son Haldrath would take one of Nidhogg's Eyes and became the first Azure Dragoon (the other going to Ishgard) which he would keep even in death until recent events. All Dragoons, both Azure and not would come from this moment.