Nobody's mentioned the Left Hand Seat yet
Okay.... The seat to be occupied by the pilot flying
may be specified for the type - or may not. The Cessna Caravan is the only single Cessna I'm aware of for which the seat to be occupied by the pilot is specified. I cannot speak for other types.
what happens if one pilot logs the first half of the flight and the other the second half?
A few things:
Neither pilot completes a whole flight, so morally cannot claim a flight's worth of experience for the time logged.
One of those pilots might not have legitimately flown the aircraft in the sense of being insured for the flight, current in the aircraft, and entitled to fly the aircraft by its owner.
At least one of the pilots did not take responsibility for the flight in a PIC sense (there was someone else there to babysit them). I note that experience I have had while flying alone, or in the company of non pilot pax has been much more valuable in terms of building confidence and experience than while I was a second pilot. On your own, it's up to you - that's what makes a pilot!
Pilots who play games with their record of experience embarrass us all....