Procedure
Diagnostic Procedure
A diagnostic procedure is one aimed at making a diagnosis, or medically "finding out what is wrong". Sometimes a Diagnostic Procedure can also be therapeutic; the doctor performing the procedure may be able to perform some treatment or intervention after diagnosing the problem.
Surgical Procedure
A surgical procedure is an operation. Typically this involves a General or Local Anaesthetic and some form of surgery, including laparoscopic or "keyhole" surgery.
Specialty Procedure
A specialty procedure or 'medical' procedure (as opposed to 'surgical') is an intervention that provides some treatment, without the need for surgery.