Air travel within Europe

From London to Amsterdam: yes, since the UK is not a part of the Schengen zone. Barcelona to Venice: no, since Spain and Italy belong to it.

Yes, these are all international flights, London and Amsterdam are in two different countries, as are Barcelona and Venice.

• London to Amsterdam: The UK is not in the Schengen Area, and the Netherlands is, so you will go through Immigration control (passports) when you land at Amsterdam Schiphol. You then pick up your luggage, but you do not go through customs as both the UK and Netherlands are in the EU (at least until March 2019). But customs is a random check only.

• Barcelona to Venice: Both Spain and Italy are in both the Schengen Area and in the EU, so no passport checks and no customs between these two countries. The airline will still want to see your passport as an ID check.

Thank you very much for your help. I appreciate it.

You can technically call them international flights because they are between countries. But for flights within the Schengen zone area they are just like flights in the US between states with no checking of passports for immigration purposes or customs.

Almost any airline these days will check your passport for its own purposes.

Being in the EU, are these considered international flights with the
same customs and passport checks as if we were flying from the US?

What customs checks? Unless you have purchases to declare, it's a walk through.