ISO 9001:2008 certification requires an understanding of the ISO 9000 standards as well as some basics on quality management systems. Here is the information you need for ISO 9001:
Understanding ISO 9001 Training will teach you how to implement ISO9001
ISO 9001 Presentation Materials review the complete standard with your organization.
ISO 9001 Certification refers to a written assurance (the certificate) by an independent external body (Certification Body=CB=Registrar) that it has audited your quality management system and verified that it meets the ISO 9001 requirements.
ISO 9001 Registration means that the auditing body recorded the certification in its client register. Learn about selecting an ISO registrar
So, the organization's management system has been both certified and registered.
Therefore, in the context of ISO 9001 both are acceptable and used interchangeably:
On the contrary, "ISO 9001 Accreditation" is not an acceptable alternative for certification or registration, because it means something different. They should be IAF approved. ISO 9001 accreditation refers to the formal recognition by a specialized body - an accreditation body like the IAF — that a certification body is competent to carry out ISO 9001 certification.
Basically accreditation is certification of the certification body. Who can grant certification?