A semi-automated AED and a fully automated AED both detects for two particular abnormal heart rhythms that are common with cardiac arrest (i.e. the heart has stopped beating normally). The two abnormal heart rhythm are ventricular tachycardia (FT) and ventricular fibrillation (VF). Once either of these abnormal heart rhythms are detected, the AED will charge up its capacitor and initiate an electrical charge to the heart. The function of the charge is to depolarize a critical mass of the heart to stop the abnormal heart rhythm and allow the heart to re-establish a normal heart rhythm again.
The only difference between a semi-automated AED and a fully automatic AED is how the electric charge is initiated. A semi-automated AED requires the rescuer to push a button to send the charge to the casualty. The computer in the fully automatic AED will send a charge to the casualty without any action from the rescuer.
When the AED detects a VT or a VF heart rhythm, the AED will inform the rescuer and charge up its capacitor. A semi-automated AED will tell the rescuer to press the "flashing shock button", and once pressed, the electrical charge will be sent to the casualty. A fully automatic AED will tell the rescuer, "shock required"; there will be short countdown (depending on the AED model, the countdown may be audible); then the AED will send the electrical charge to the casualty.
Some people prefer a semi-automated AED because they can ensure that no one is touching the casualty before pressing the shock button to shock the casualty. Others prefer the fully automatic AED because they feel they may hesitate to shock another person (or just don't want to be responsible for initiating the shock).
Some AED models are only semi-automated (e.g. Philips Heartstart Onsite, Physio-Control LIFEPAK Express). Many AED models have both semi-automated and fully automatic versions (e.g. Cardiac Science Powerheart G5, Zoll AEDPlus).
There is no real advantage of one version over the other. Once the customer understands the difference between semi-automated and fully automatic, it comes down to user preference, availability of the version in stock, and the customer's willingness to wait (if a particular version is not in stock).
The following video is produced by Zoll and shows you the difference between their semi-automated AEDPlus and their fully automatic AEDPlus: