Immobilizer is not the same as the alarm. Although, they're both used for theft prevention, they however serve two different functions.
Alarms are primarily used to prevent unauthorized entry into the vehicle.
On the other hand, immobilizers are used to prevent usage of the vehicle, even if the thief has an exact physical duplicate of the original key. Immobilizers makes use of transponders hidden inside the original key's handle. As you turn the ignition key to ON, the vehicle's immobilizer system queries the transponder. The transponder would then respond with the correct code wirelessly. If the wrong code is received or if there's no code at all, the engine will not start.
Some alarms emulate the function of an immobilizer by cutting off the ignition while it is armed.
Here's a short demonstration of how it works:
YouTube - How the Immobilizer Works