Private Owner Versus Charter/Airwork Pilot
It would appear that a Private Owner Pilot can do what they (the pilot singular or plural, male, female or other gender(s) as applicable) likes, within the constraints of Schedule 8.
A pilot working for an organisation that has an AoC would not be able to do the same as the Private pilot, unless an approved/authorised person has deemed them (the pilot singular, male, female or other gender(s) as applicable) competent to carry out the task as listed singularly, and by Job Number.