duty free

It depends on the airline, the terminal, and if the plane is docked within the same sector of a terminal. Even if the plane is scheduled to dock at one door, it could be moved elsewhere to a different terminal at the last minute.

Not completely sure of your question given your comment about the Boston flight. It is my understanding that you can only buy duty free when leaving the country. Paris to Madrid would be a local flight and not international until you left Madrid. Have no idea or understanding of why something would be confiscated in Dublin that was bought in Boston. Unless you are asking about wine and having to go through security again.

Isn't Paris to Madrid international? Are they different because they are both European?

All flights in western Europe are consider local or domestic.

"<<All flights in western Europe are consider local or domestic.>> I believe this only applies to intra-EU flights." It only applies to flights within the Schengen zone. The UK, for instance, is in the EU but not in Schengen. Both France and Spain, however, are in Schengen.

<<All flights in western Europe are consider local or domestic.>> I believe this only applies to intra-EU flights. There are still a few western European countries that are not in the EU, such as Norway, Iceland, Switzerland, Croatia. I think the legal distinction between "domestic" and "international" mainly has to do with which country's (or international entity's) liability laws will apply in case there's an accident.

And flights between London and Rome or Germany, etc. are consider domestic. And just to keep the confusion going, train travel between countries is considered international.

My memory isn't as good as it used to be, but I recently flew London-Lisbon and Nice-London, and I'm pretty sure I went through immigration control. From the British Foreign Office website: "Entry Requirements - Passports
You need a passport valid for the proposed period of your stay to enter France." Nothing about not needing a passport if you fly instead of taking Eurostar. Says the same for Germany, but not for Ireland, because of something called the Common Travel Area, but that just includes Ireland, Great Britain, the Isle of Man and the Channel Islands.

The UK and Ireland are the exception to the rule as they are the only two countries in western Europe that haven't signed on to the Schengen agreement; so there are indeed immigration controls between the UK and the rest of Europe. But for everywhere else, flying from say Helsinki to Lisbon, is the equivalent of flying from LA to NYC here in the US.