Please note: This AC CDI, not DC CDI.

AC vs DC fired or pulsed CDI IGNITION SYSTEMS

Here is the readers digest of how a CDI works

In all cases there is a magnet that passes a magnetic coil and induces a pulse in that coil which then is wired to the CDI and causes the small induced pulse to fire an electronic device (there are more than 1 type but this all happens inside the CDI) Which discharges the larger pulse stored in a capacitor. This larger output pulse is wired to the coil where the large pulse is able to make the coil function as a voltage increasing transformer thereby producing the very high voltage necessary to create a spark across the gap of the spark plug.
Now for the 2 main type of CDI used in the 49 cc scooter market, AC and DC Both function essentially the same. With the AC unit, alternating plus and minus varying voltages are used to charge the capacitor described in the paragraph above. The DC unit takes 12 volts more or less DC from the battery and that voltage is used to charge the capacitor described in the paragraph above.
Pros and Cons:
AC unit allows the engine to run without the need for a battery or charging system of any kind.
DC unit was created to allow higher RPM ranges due to the instantaneous availability of the Charging current. Where the AC one has lots of complex and difficult to explain things like coil flux density and residual decay etc.
The wiring is different also usually but not always, the ac ones have a rectifier or diode ahead of the CDI and the DC ones just connect directly to the battery.
the way to tell for sure is to turn on the key and see if 12v is present at the CDI assuming all else is correct. Some units that are DC include:
Kymco Agility 50, Diamo Velocity, Vento Triton, Schwinn, Tomos, and other high end Chinese, Korean, and Taiwanese scooters.