Several EU countries such as the UK, France and Netherlands have territories and dependencies outside of Europe. Examples include many islands in the Caribbean, Falkland Islands, Tahiti, and so on.
These have a complex relationship with the home country (usually a former colonial power), and with the European Union. Some are inside the EU for some purposes, some are not. Who can live and/or work in the territory is complex, even for citizens of the home country.
Given this, which territories of EU countries, outside Europe, are somewhere that any EU citizen could move to, to live and work, under the EU freedom of movement?
For example, Aruba is one of the four countries in the Kingdom of the Netherlands. Does that make it part of the EU for residence? Are any of the French DOMs and TOMs, like French Polynesia, areas that EU citizens have the right to settle in? Are any of the overseas UK territories, such as Anguilla, part of the EU for residence?