Some of it might be terminology issue. For me, a training flight is a flight that is written with appropriate "exercise" number into logbook and is part of the

Some of it might be terminology issue. For me, a training flight is a flight that is written with appropriate "exercise" number into logbook and is part of the official training program. These days most airlines do those on simulators, and they will include "rarer" operations like rarely used approaches (2xNDB instead of ILS, how to fly DME arc approach, etc), instrument failures, and so on. You do not do such flights with passengers, because you're intentionally lowering the safety level. In addition to that, there's a recommendation to randomly, given safe conditions, do regular manual operations. Mind you, those SOPs probably explicitly say "do not experiment after long haul flight". I might have been a bit more cross because people have died (including in ways that impacted me) because of organizations that mixed "training" and "passenger" flights.