An Instructor gives Instruction if a pilot is current on type and having a flight to demonstrate that they are safe then they are not recieving Instruction and so they are P1 and Instructor is just an observer and should log nothing.
If the pilot requires Instruction during the flight on an aspect of the flight then they are being given Instruction.
When I check someone out current on type I state at the start of the flight they are in command and I am just there to observe they are safe to meet the insurance requirements. If I see anything during the flight that is unsafe then I will state I have control and that I become pilot in command, the flight then becomes a training flight.
If I am checking someone out who is current on class but is new to type then I would hope I am teaching them something specific to that aircraft and then it a training flight and they are PUT.