Final answer:
The numbering system where a patient retains the same identification number for all visits to a healthcare facility is a static patient identification system.
Step-by-step explanation:
The numbering system described in the scenario, where Annie Smith was assigned a patient number 123456 and reassigned the same number upon returning to the hospital, suggests a consistent or static patient identification system. In this type of system, once a patient number is assigned, it remains with the patient for all future visits and interactions within the same healthcare facility or system. This approach aids in maintaining continuity of care and the integrity of medical records. In contrast, a dynamic or sequential numbering system would assign a new number with each visit.