Technically, I think their definitions are similar enough that you can use either to have the correct meaning conveyed. "To settle" has more of a connotation of "to complete", or "to resolve". When talking about location, it means "to move-in" or "to live permanently in a place". "To establish" has more of a "to create" kind of feel to it. Like to create a new organization or group.

Yes, they are very different. To settle is usually used to mean that a problem is resolved. "They settled their argument." (they are no longer fighting) "It's settled then, I'm going to Brazil!" (I've decided to go to Brazil; I'm no longer unsure.) In a historical context, settled means to create a community in a new place. "The English settled the eastern coast of the New World." Established is a more technical term that is often used in law or to describe an abstract concept. You can think of it as meaning "to create," or "to discover." "The Constitution forbids an establishment of religion." (to create a national religion) "They established a motive for the murder." (to discover the reason for the murder) I hope this helps! Buena Suerte! Greg