Examination specifically means QC activities such as an NDT activity. It is not an inspection. Inspection means verifying a QC activity by either witnessing it or repeating the QC activity.
The closest analogy could be the difference between a laboratory blood test (examination) and doctor’s diagnosis (Inspection which includes evaluation and interpretation or acceptance/rejection).
Examination reports shall be approved by the API inspector.
NDT technician examines the material by an NDT method and reports the result.
NDT examiner can also report the acceptance or rejection of a material or equipment against an approved acceptance criteria if authorized by the inspector.
In any event, it is the inspector who shall approve the examination report.
Please remember that the API inspector is the final authority in accepting or rejecting the QC and NDT examination reports because it is the API Authorized Inspector that certifies the vessel is fit for service.