What term can I use to express the delay between two connecting flights in the following situation: I fly down to one airport and wait there without exiting until I take another flight to reach my destination.
In American English, this is often called a layover,
a short stay somewhere between two parts of a journey
In my experience, it is most commonly used to describe a wait of several hours between flights or trains, during which you often do not or cannot leave the transit hub. How long is your layover in NYC? Can we meet for lunch?
Layover is sometimes used to describe an overnight stay, but in American English I would tend to ask, instead, How long are you staying? if I expected the answer to be that you were staying at least one night.
You can call the wait a stopover.
A Layover, in my experience, has always meant a long time between flights (enough to possibly eat, or stay over night in a hotel).
If I'm just changing planes (e.g., Flying from Cleveland to Orlando, but need to catch a connecting flight in Baltimore in, say 1-2 hours), that's merely a "connection."
If I have that same flight, but the time between flights is more like 4+ hours, I'd call that a layover. Overnight is definitely a layover. Airlines call that overnight a "stopover," but to me, it's always been a layover.
Over time, I think the term Layover has come to mean ANY connecting flight, even if it's only 1 minute. I think its meaning has changed over time.