It is not semantics in the least. A "connection" is a term of art. On a missed connection, the late delivering carrier is responsible for rerouting you. If it is a "community" (EU) carrier or the flight originated in the EU, that carrier may have duty of care and delay / cancellation compensation obligations all dependent on the arrival time at the final arrival time at the connection flight's destination.

If you take even a glance at FT, you will see thousands of threads from travelers who state that they were sold a single "itinerary" by a TA and that they missed their "connection" and were forced to buy a new ticket by the onward carrier. When asked, it turns out that the PNR contained two tickets, and that they were not connecting.

Thus the differentiation is very real and has very real consequences for many unsuspecting consumers.