air travel – In what case doesn’t a coupon correspond to a segment?

A coupon is a discrete component of a ticket that is separately valued and separately redeemed. It’s the record that you’ve paid for a portion of the trip, and the record as to whether you’ve used it or not. An airline segment by the IATA definition is a passenger enplaning and deplaning, though this term is used more loosely by lay people, and gets confusing in the GDS world where you can have “hotel segments” and so forth.

An itinerary can have gaps or “land segments/surface segments” as lambshaanxy notes, as on an open jaw or RTW ticket. The airline is not transporting you between those points, nor any other carrier on the ticket. They count as segments, but there would not be an associated coupon.

Most “direct” flights nowadays are indistinguishable from connecting flights, but it may be possible that you have a single coupon for multiple segments as well.