PsyBA is the national organisation responsible for determining who is suitable to be registered to work as a psychologist. If you wish to be employed by an organisation or operate your own practice as a psychologist, you must be registered with the Board.
The APS is a professional body representing psychologists and is not responsible for registering psychologists. So whilst you must be registered with the Psychology Board of Australia, it is up to you to choose whether or not to become a member of the APS. For more details about the APS, visit their website www.psychology.org.au.