As a technicality, I would suggest that a "trainee" is a person to whom a new skill or qualification is being imparted by a "trainer". As distinct from a "check flight" where one qualified pilot, is checking the competence of another qualified pilot. Additionally, in Australia, we have a definition of ICUS (In Command, Under Supervision) ... whereby one pilot is qualified to conduct the flight, but for regulatory, contractual or company requirements, must be supervised by a second (usually more experienced) pilot. Does anyone here know what the nature of this flight was?