While working with the DICOM study, series and media concepts, I wondered if these values are to be unique over all data, or only to the patient they belong to.
Phrased otherwise; can I have 2 patients having a study/series/sop instance uid that is the same value for both patients?
Or does the DICOM standard simply doesn't care about that and is that open to the implementor to decide?
In DICOM, a Study (identified by its Study Instance UID) is always associated with a single Patient. See DICOM standard part 3 for details.
To answer your initial question/thought: a Unique Identifier (UID) has to be globally unique, i.e. world-wide over all patients, devices, hospitals, etc.