I'm a CX FO who is qualified to relieve the Captain in cruise. When I'm in the seat as PF or PM I log it as SIC. The Hong Kong "FARs" are different than the US in how we log time. When I relieve the Captain I log it as "PIC under instruction" per Hong Kong rules. I only log time in the seat not the entire flight.
The SO's log what's called P2X time, it's not SIC. There really isn't a US equivalent, its sort of "SIC under instruction" but hopefully some of the American SO's will chime in and say how the log it.