Many people use ‘Accreditation’ and ‘Certification’ interchangeably, but they are not the same.
Certification is a technical review that assesses the security mechanisms and evaluates their effectiveness. Accreditation is management’s official acceptance of the information in the certification process findings.
For example, if a company is planning to undergo an ISO 27001 certification. The company can be certified by a company like BSI and say that they meet the criteria for a successful ISO certification, but the company will also be accredited by an external organization to state that they are good enough to perform the tasks of an ISO 27001 required vendor.
The bottom-line is if a company is certified on the ISO controls, they should be accredited as well when they will receive the final certificate (read acceptance) from the certification body.