When legally "current" and "actual" on a (biannual or other) checkride with FI you log time as PIC resp. P1, because that is what you are - in command.
If on a renewal flight, because something expired, or you add items to your license and fly with an FE in her/his role as an examiner, then you are PuT - under training and the FE is responsible pilot.
Example: if you fly your renewal checkride within 90 days before expiry, you only need an FI to sign you off and you will keep the old date for renewal plus two years. If you are outside 90-days-rule, either b4 or later, you will have to have a ride with an FE and will get a new time line day of checkride plus two years.