Accreditation body follows the standard ISO 17011. On the other hand CB follows the ISO 17021 Standard. Both the standards have come from ISO.
AB can be government or non-government. Both of them’s job is the same. There is no direct link of AB with customers. So, it is not your responsibility to know too much about AB.
However, accredited certificate has good value. So, before going to get your certificate you will have to be sure that you are going to get accredited certificate from your CB. Because there are two kinds of certification body: one is Accredited Certification Body and another one is Non- Accredited Certification Body.