The Auto Hold, and parking brake are two separately operated system. I love auto hold, it is one of the many advantages of an automatic, it simply applies when your braking and the car comes to a standstill, releases when you operate the throttle. Hence your brake lights are on, as the brakes are applied.
When the parking brake is applied, the system engages just the rear disc brakes. Some manufacturers used to have a separate, small, drum and shoe system, within the rear brake disc for the handbrake/parking brake, but many done away with that when I was in the motor trade……..and that was decades ago!