> They do if it's an international connecting flight (that is, if the change occurs at the port of entry)Yes, that's true; but that's not a reason to prefer direct flights that are domestic only, which a lot of US air traffic is. Other parts of the world do differ, yes. (Although I wonder: do international flights within the EU still require re-screening if you make a domestic connection? There's no passport control or customs, right?)
> our if the flights are in different terminals in the same airport
...and the airport doesn't have a way of going from terminal to terminal without leaving the secure area; but lots of airports, particularly those with a lot of connecting flights, do have that (either a train or shuttle bus).